Journal of Mathematical Modeling and Fractional Calculus
The Journal of Mathematical Modeling and Fractional Calculus is dedicated to providing a platform for researchers to publish high-quality research articles that apply mathematical modeling principles to solve real-world problems across various scientific disciplines. The journal focuses on new mathematical challenges and their applications in applied science, contributing to the advancement of scientific knowledge within the community.
A CaputoUFabrizio Fractional-Order Tumor ˝ UImmune Interaction Model with Treatment and ˝ Immunotherapy: Stability, Optimal Control, and Sensitivity Analysis
We present a fractional-order immune tumor interaction model that captures both tumor progression and treatment effects under Caputo Fabrizio (CF) derivatives (a non-singular kernel fractional derivative). The model divides the system into five key compartments: naive immune cells, effector immune cells, viable tumor cells, treatment-affected tumor cells and dead tumor cells. It incorporates tumor logistic growth, immune activation, proliferation, immunotherapy infusion, drug-mediated cytotoxicity, relapse, and clearance processes. The frac tional formulation reflects memory and hereditary properties inherent in biological interactions. Mathematical analysis establishes equilibrium points, derives the basic reproduction number and determines stability condi tions for tumor-free and coexistence states. Numerical simulations support the theoretical results and reveal the influence of fractional order and therapeutic parameters on tumor suppression and long-term immune control. This framework bridges rigorous mathematical modeling with clinically relevant insights, offering guidance for optimizing immunotherapy and improving treatment strategies.
Copyright (c) 2026 Journal of Mathematical Modeling and Fractional Calculus
Analysis and investigation of complex network immunity waning and two strain dynamical system
Some epidemic illnesses, like Zika virus and COVID-19, have several strains of the pathogen, mak ing disease control difficult and leading to complex dynamics. We do not know, however, fully comprehend the dynamic characteristics of interacting numerous strains. Vaccination is the most efficient method of out break control since it reduces the actual amount of illnesses and creates herd immunity. In order to do this, we proposed the two-strain epidemic model, which shows that immunity declines in a complex network and vac cination is not flawless. The critical values are then further determined in order to confirm the global stability of each strain dominant equilibrium point. Proposed mathematical model is investigated by bounded solution, positive and unique solution which are major characteristic of the epidemic model. To confirm the rate of spread under different conditions, the verge condition which incorporates sensitivity analysis is also developed. Caputo fractional operator is utilized for numerical solutions under different fractional values. Lastly, the outcomes of the theoretical study have been seen by numerical simulations for the developed solution. Understanding the dynamics and behaviors of multi-strain epidemics is made easier by the current findings.
Chaos, bifurcation and statistical analysis of rubella disease dynamical system by utilizing different fractional approach
Rubella is a virus cause serious health problems, particularly for expectant mothers and their unborn children. Understanding its dynamical transitions is crucial for elimination strategies. In this paper, we sug gest SVEIR model Rubella model that captures the lifelong immunity after natural infection acquired through vaccination. This work presents the dynamics of Rubella spread using fractal fractional Mittag Leffler operator and Atangana Baleanu Caputo operator. Both of the operators provide reliable solutions in simulation, while the fractal fractional derivative provide better results then ABC operator due to its fractal structure solved through Newton polynomial based numerical approach. A comprehensive mathematical examination of the suggested model is presented, covering existence of bounded and positive solution, convergence and stability. We also prove the existence of transcritical bifurcation at R0 = 1 using center manifold theory, which determines the threshold between disease elimination and endemic persistence. We provide impact of parameters through 3D bar plot that shows transmission rate and vaccination rate are very important in Rubella disease dynamics. The chaos test shows that model experiences bounded behaviour and does not exhibit chaotic oscillations. The sta tistical analysis provides information about symmetric behaviour of the compartments of the model. The work serves as a complete reference for mathematical modeling of rubella control.
Period-Doubling and Neimark-Sacker Bifurcations in a Discrete Fractional Predator-Prey Model with Harvesting
This paper investigates a discrete-time fractional-order predator-prey model with proportional harvesting on the prey population. The model is derived using the piecewise constant argument method, allowing the incorporation of memory effects in a discrete framework. The existence and local stability of equilibria are analyzed via the Jacobian matrix and characteristic equation. Conditions for period-doubling and Neimark-Sacker bifurcations are established, revealing transitions to periodic and quasi-periodic dynamics. Numerical simulations illustrate the impact of harvesting intensity on system stability and oscillatory behavior. The results highlight the significant role of harvesting and memory in shaping predator-prey dynamics. Keywords: Population model; fractional derivative; harvesting; stability; bifurcation
Reproduction Number and Stability of a Caputo Fractional Derivative Immuno-Metabolic Infection Model for Cats with Obesity and T2DM Effects
We have study chronic inflammation, obesity and type 2 diabetes mellitus (T2DM) [33] are increas ingly recognized as key immuno-metabolic determinants of host susceptibility, infection progression, and recov ery in companion animals. Motivated by these mechanisms, we formulate a fractional-order immuno-metabolic epidemic model for infection transmission in cats stratified by metabolic health status. The model employs Ca puto derivatives of order 0 < ξ < 1 to capture memory-dependent immunological and inflammatory dynamics, including adipokine-driven chronic inflammation, obesity-induced metabolic impairment, and T2DM-associated immune dysfunction. The feline population is divided into metabolically healthy and metabolically impaired groups, each with susceptible, infected, and recovered classes, together with an additional variable describing systemic inflammation. Using the next-generation matrix method, we derive the basic reproduction number R0, explicitly decomposing contributions from healthy and metabolically impaired hosts. Analytical results show that metabolic impairment and inflammation enhance transmission through increased susceptibility and infec tiousness. Within a fractional Lyapunov framework, the disease-free equilibrium is locally and globally asymp totically stable when R0 < 1 and unstable when R0 > 1. The proposed model provides a rigorous mathematical framework for quantifying how chronic inflammation and metabolic disorders modulate infection dynamics in feline populations, underscoring the importance of incorporating immuno-metabolic factors into epidemic mod els to improve disease burden prediction and design targeted interventions for cats with obesity and T2DM. And plot the figure by the help of python.
Nanofluid flow, heat and mass transfer over a linear stretching surface under convective boundary conditions by considering MHD and chemical reaction effects is three-dimensional
This paper addresses Transport of heat and flow in dimensions behaviour of a Williamson nanofluid flowing across a porous layer for extending under the influence of magneto hydrodynamic (MHD) forces, heat rays, Darcy Forchheimer resistance, and chemical reaction influence. The governing nonlinear partial differential equations were abridged to similarity transformations into ordinary differential equations and to solve them systematically by the optimum Technique of homotopy investigation (OHAM). Effects of thermophoresis, Brownian motion, Deborah number, Prandtl number, porosity factor, Forchheimer number, and chemical reaction in addition radiation parameters taking place velocity, temperature and concentration profiles were studied in detail. It shows that velocity field is reducing in porosity, Forchimmer number, and magnetic parameter whereas stretching parameter improves the flow. Moreover, porous and inertial effects suppress the drag forces but the Williamson parameter enhances them. Larger values of Prandtl number, Chemical reactions with rays increase the rate of heat transfer whereby, the Brownian principle and thermophoretic diffusion reduces it.
Control of Marburg Virus Disease Spread in Humans under Hypersensitive Response through Fractal-Fractional
In this study, we propose and analyze a novel fractional-order preypredator-super predator model that incorporates maturation delay, harvesting, and the Allee effect. The prey population is assumed to grow logistically under the influence of a strong Allee effect, with a time delay accounting for the mat uration period. Predators and super predators interact through predation and competition, while also experiencing harvesting impacts. The system is described using the Caputo fractional derivative to bet ter capture memory effects inherent in ecological processes. Furthermore, herd behavior in predation is represented through a generalized functional response dependent on a parameter α, modeling various herd structures such as circular, square, cubic, and spherical formations. Key parameters include the intrinsic growth rate of prey, carrying capacity, mortality rates, predation coefficients, Allee threshold, and harvesting intensities. We investigate the existence and local stability of equilibria, derive the net reproduction numbers for both predator and super predator populations, and perform a Hopf bifurca tion analysis to explore the emergence of delay-induced periodic solutions. The results enhance the understanding of how memory, delay, harvesting, and Allee effects collectively influence the dynamics of ecological systems. The AdamsBashforthMoulton method is employed to approximate the solutions of the proposed model. Using Python, we perform graphical illustrations and numerical simulations to support our analysis.
Functional Quantum Calculus: Theory and Applications via q(t) and h(t)Operators
This paper introduces a novel framework for functional quantum calculus based on generalized q(t) and h(t) calculi, with applications to geometric function theory and special functions. We define q(t) – exponential, Gamma, Beta functions, hypergeometric series, Hermite polynomials, and starlike/convex functions, along with formulating q(t)- and h(t)- differential equations. Key contributions include establishing the relation between h(t)- and q(t) – derivatives and the fundamental theorem of h(t) – calculus. We also prove orthogonality for q(τ) – Hermite polynomials and provide numerical examples.
Analytical Investigation of Hopf Bifurcation and Intrinsic Nonlinear Dynamics in a Fractional-Order HIV/AIDS Transmission Framework
We propose and analyze a fractional-order HIV/AIDS transmission model that partitions the popu lation into susceptible men and women, undiagnosed and diagnosed infected individuals, AIDS patients, those undergoing treatment, and cumulative mortality. Incorporating demographic and epidemiological data from South Africa and India, parameter estimates are adjusted to capture regional variations in HIV prevalence and treatment coverage. The model ensures biological plausibility by demonstrating the positivity and bounded ness of all solutions. The disease-free and endemic equilibrium states are derived, with the basic reproduction number R0 formulated through the next-generation matrix approach. Stability analysis both local and global are conducted using RouthUHurwitz criteria, and conditions for Hopf bifurcation are identified to reveal potential ˝ oscillatory infection dynamics. The existence and uniqueness of solutions are assured under a Lipschitz con dition. Overall, this framework offers a rigorous mathematical foundation for understanding HIV transmission mechanisms and informing intervention strategies in heterogeneous populations.
Dynamics and control of a fractional fractal Mittag-Leffler SV EI1I2R model for Lumpy skin disease
In this Study we extend the work of Reem K. Alhefthi [12] on Lumpy Skin Disease (LSD) dynam ics using symptomatic and asymptomatic measures with a Mittag-Leffler kernel, we propose a fractional fractal Mittag-Leffler SV EI1I2R model to capture memory and hereditary effects in disease transmission. The mod elŠs dynamical behavior is rigorously analyzed, including local and global stability and the basic reproduction number. We derive conditions for Hopf bifurcation, revealing scenarios that may trigger oscillatory outbreaks. A detailed sensitivity analysis identifies critical epidemiological and control parameters that significantly influ ence disease spread. Additionally, an optimal control framework based on PontryaginŠs Maximum Principle is developed to minimize infection via vaccination, treatment, and isolation strategies. Numerical simulations demonstrate the profound impact of fractional-order dynamics on epidemic progression, offering insights into the interaction between bifurcation phenomena, parameter sensitivities, and optimal interventions. This study provides a robust, integrated framework for understanding, predicting, and controlling LSD in livestock popula tions.
A Brief Review of The Development of The Theory of Dynamical Systems
In this paper, we present a brief analysis of the evolution of theories of dynamical systems applied in various mathematical Models. In this study, the contributions of some notable mathematicians have been extensively discussed in the context of multiple applications of mathematical theories to dynamical systems. The investigation of the stability of periodic solutions, the stability of equilibrium, and Poincaré‟s periodicity has also been discussed in this paper. Moreover, an extensive study has been carried out on a brief application of the Poincaré Maps, the Last Geometric Theorem, the Restricted Three-Body Problem, the Generalized Hopf bifurcation, and the Van der Pol and Lienard equation for various mathematical models applied in dynamical systems.
A CaputoFabrizio Fractional-Order SEIHRVN Model for Human Metapneumovirus (hMPV): Vaccination, Stability and Sensitivity Analysis
Human metapneumovirus (hMPV) is a major cause of acute respiratory infections across all age groups with no licensed vaccine currently available. To capture the disease dynamics and assess potential control strategies we propose a fractional-order CF–SEIHRVN model incorporating seasonal transmission, hospitalization, waning immunity and vaccination. The model stratifies the population into Susceptible (S), Exposed (E), Infectious (I), Hospitalized/Severe (H), Recovered (R), Vaccinated (V) and total population size (N). Caputo–Fabrizio fractional derivatives are employed to account for memory effects in transmission and recovery processes. Key epidemiological parameters are drawn from demographic and clinical data for China and India. Seasonal forcing in β(t) reflects climatic in fluences on transmission. The framework enables computation of the basic reproduction number R0, stability analysis of equilibria, Hopf bifurcation investigation, and optimal control formulation. Sen sitivity analysis highlights key parameters affecting R0. Numerical simulations illustrate intervention strategies providing valuable insights into hMPV control under different demographic conditions.
Some Fractional Calculus Operators Associated with Generalized Mittag-Leffler Funcitons
In this paper we have evaluated some new results with Saigo fractional integral operator first and second kinds involving generalized Mittag-Leffler functions and also evaluate the new theorem with special cases.
Investigation of COVID-19 epidemic mathematical model incorporating media coverage impact and control
In order to estimate and control the recent corona virus disease 2019 outbreak, under me dia impact. Most countries impose stringent intervention measures to halt the spread of COVID-19. Globally, the COVID-19 epidemic has raised a lot of concerns. A non-smooth SIR system is proposed to investigate the impact of three control strategies (vaccination, therapy, and media coverage) on the spread of an infectious disease. Social media platforms like Face book, Twitter, and others have been crucial in spreading information during the COVID-19 outbreak, both factual and misleading, which has led to widespread confusion. When the susceptible population surpasses the threshold value, the traditional epidemic model comprises media coverage, linear functions that describe vaccine injection, and treatment tactics. COVID-19 model under media coverage investigated both qualitatively and quantitatively. models key proportion are also verified like boundedness, uniqueness and existence. Stability Analysis his also know development on local and global scale in order to properly manage funds and human resources and create successful disease preventive marketing efforts, organizations, institutions, enterprizes, policymakers, and educators who are in charge of infection and disease control must keep a close eye on infection rates.
Copyright (c) 2025 Journal of Mathematical Modeling and Fractional Calculus
Analysis and treatment impact to control the transmission dynamics of skin sores disease with novel hybrid fractional operators
Skin sores (impetigo) are a frequent and contagious skin infection in young children, caus ing blisters and ulcers. It is usually not hazardous and resolves within a week of treatment or a few weeks if no treatment is used. Treatment is commonly recommended since it can shorten the length of the condition and reduce the risk of the virus spreading to others. We developed and tested a non linear hybrid fractional order model to investigate skin sores infection and the transmission dynamics. The study examines the mathematical properties of the suggested model, such as the feasible region, equilibrium points, basic reproduction number, and existence of the system’s unique solutions using Banach fixed-point theory. It also uses the appropriate lyapunov function to examine the stability of equilibrium states. This work gives a thorough examination of several hybrid fractional operators and numerically simulates the suggested skin sores system using the Laplace-Adomian decomposition approach, demonstrating its efficacy in simulating theoretical scenarios. This research advances our knowledge of the mechanisms underlying disease transmission by taking into account fractional-order dynamics and a variety of routes, offering suggestions for better disease management and control.
Dynamics of a Food Chain Model Using the Caputo Fractional Derivative
This work investigates a fractional-order food chain model based on the Caputo operator, taking into account resource availability, competition, and predation. The dynamics of the food chain are bet ter represented using fractional calculus, which takes into account long-range interactions and previous dependency. Analytical and numerical simulations reveal information about the resilience, persistence, and stability of biological communities under fractional order dynamics. The model includes a three species food chain, as well as environmental contamination. We begin by confirming the model’s uniqueness, nonnegativity, and boundedness. We also examine numerous conditions for the presence of equilibrium and local stability. Second, a controller is proposed, and the global stability of the positive equilibrium point is investigated using the Lyapunov method. The proposed model solution was estimated using the fractional iterative technique, and numerical simulations were carried out to validate the theoretical results.
Finite Volume Simulation of Nanofluid Heat Transfer with Free Slip
This study numerically investigates the viscous heating mechanism in a nanofluid-filled cavity subjected to external forces applied to the top lid, combined with laminar mixed convection of the nanofluid. The vertical walls of the cavity are assumed to be insulated, non-conductive, and impermeable to mass transfer. The horizontal walls are differentially heated, with the lower wall maintained at a higher temperature while the upper wall remains cooler. The primary objective of this research is to introduce a novel method that accurately incorporates height in the solution of heat transfer equations, using transient analysis for numerical iterations. Although the fluid flow reaches a steady state, the square cavity’s walls are fully insulated, and a constant heat flux is generated by the motion of the top lid. This work aims to analyze the effects of viscous heating in a fully insulated lid-driven cavity with Neumann boundary conditions under both no-slip and free-slip conditions, while varying Rayleigh and Prandtl numbers as independent parameters. The simulations are performed for a specific case where the Prandtl number Pr = 6.2 is fixed, while Rayleigh numbers and the volume fraction of the nanofluid (water mixed with copper nanoparticles) range from 0% to 5%. The time dependent vorticity-stream function and thermal energy equations are discretized and solved using a custom finite volume method combined with the artificial compressibility approach, implemented in MATLAB. Despite viscous heating having a limited effect, the Neumann boundary conditions with no-slip and free-slip assumptions influence heat retention within the insulated cavity. The free-slip condition acts as a lubricant, leading to reduced temperature distribution, particularly under lower Rayleigh numbers and higher Prandtl numbers, compared to the no-slip condition. This is attributed to the free-slip effects under these conditions, which enhance heat dissipation and increase the fluid velocity, further stabilizing the system.
On Double Delay Terms Robbin Boundary Value Problem with Fractional Derivative
In this manuscript, the existence theory of a mixed delay Robbin boundary value problem (RBVP) together with impulsive conditions is investigated. For the required results, we use topological degree of non-compactness. The concerned tools have the ability to relax the strong compact criteria to some weaker one. As compared to fixed point theory, the aforesaid proposed tools are more powerful and applicable in dealing various nonlinear problems of fractional order differential equations (FODEs) with different kinds of boundary conditions. Proper example is given to illustrate the results.
Innovative Multiplicative Connectivity of Poly-ether Ketone, Poly-ether Ketone Ketone, and Poly-ether Ether Ketone
Organic chemistry constantly pushes the boundaries by synthesizing new molecules each year. However, before these compounds can be practically used, rigorous testing is needed to understand their characteristics. This process can be expensive and time-consuming, requiring specialized laboratory equipment, chemicals, and personnel. To address these challenges, mathematical models are increasingly used to predict the properties of compounds theoretically. In this study, we focus on polyether ketones (PEKs), calculating their atom bond connectivity (ABC) and examining their sum-connectivity and multiplicative-connectivity indexes. Our results show that PEKs exhibit notably high atom bond connectivity, which could have promising implications for their use in material science and other advanced applications.
Dimensional Analysis of the Tickysim Spiking Neural Network: Insights and Applications
Abstract: Graph theory is like the backbone of our understanding of complex networks, whether they be social, computational, or biological. In this study, we dive into the fascinating world of the Tickysim Spiking Neural Network (TSNN) to explore its metric, edge metric, and fault-tolerant metric dimensions. We aim To unravel its structure’s intricacies and uncover its potential applications. At its core, the metric dimension tells us how many vertices we need to pinpoint the locations of all other vertices based solely on distance measurements. Similarly, the edge metric dimension reveals the minimal number of edges necessary to achieve the same goal. To add another layer of reliability, the fault-tolerant metric dimension ensures that the network can still be recognized even when some vertices or edges are out of action. Throughout our research, we discovered unique symmetries and structural features of TSNN, which enabled us to identify resolving sets for both vertex- and edge-based metrics. What’s exciting is that these resolving sets work consistently, regardless of how we label the network, allowing for reliable identification even in complex scenarios. Notably, we found that the fault-tolerant metric dimension of TSNN is 3, while its metric dimension stands at 2, highlighting the network’s impressive adaptability and resilience. By exploring these dimensions, our work sheds new light on the reliability and flexibility of TSNN, emphasizing its potential for groundbreaking advancements in areas like computational neuroscience and neural network modeling. We believe these insights not only enrich the theoretical landscape of graph theory but also pave the way for innovative applications in fields that thrive on robust and intricate network designs.
Fractional Integral Operator Associated with the I-Functions
In this paper we have evaluated certain fractional integral operators associated with Saxenas I-function using the operators of fractional integration. The results obtained are of general character and are reduced to the known results on specializing the parameters. By leveraging the properties of fractional calculus, we investigate new integral transforms involving in this function. We present novel results that extend the existing theory and provide a framework for solving complex integral operators in broadening the scope in this function. These results have potential applications in various fields such as astrophysics, engineering, and applied mathematics, where the I-function and fractional calculus play a crucial role
Integrating Novel Deep Neural Networks on the Analysis of Fractional Epidemiological Models in both Populations with Disease Infection
Deep Neural Networks (DNNs) have become one of the most significant tools utilized in analyzing complicated systems, surpassing the ability to comprehend complexities. The study provides the advantage of DNNs' interest to improve the analysis of intricate patterns and produce insightful findings. It is crucial to comprehend the dynamics of infectious disease spread in ecological systems, especially when it comes from predator to prey, because of its significance for a variety of real-world situations. In complicated regulation environments, the size range of prey and predator populations is influenced by the complicated interactions between infections and predator-prey relationships. The analysis of fractional epidemiological models in both populations with disease infection (FEM-BPDI) is performed through the novel application of artificial intelligence, particularly Deep Neural Networks (DNNs). Datasets for Deep Neural Networks are generated using the fde12 solver. Training, testing, and validation phases are applied to the DNNs models to acquire solutions for the FEM-BPDI under different epidemiological scenarios. Several statistical metrics, such as mean-squared error analyses, auto correlation of error (ACE), correlation input and error (CIE), error histogram visualizations, and expected regression measurements, are used to show the efficiency that DNNs are at solving the FEM-BPDI. The model's stability and resilience in forecasting disease dynamics are highlighted by a low Mean Squared Error (MSE) that is obtained. Also, the small or negligible Absolute error provides more evidence of the suggested technique's efficacy. This study highlights the critical role that AI-powered Deep Neural Networks play in improving the comprehension and forecasting of fractional epidemiological models in the context of dual population dynamics, providing invaluable insight into the dynamics of disease transmission and ecosystem control.
An analysis of the Caputo Fabrizio fractional modeling for infectious diseases caused by chlamydia
These days, infectious illness mathematical modeling is a major global trend. With the use of current data, mathematical models enable us to predict the occurrence of disease outbreaks in the future. In this work, we use a fractal fractional operator with two fractal and fractional orders to solve a system of fractional differential equations using a Caputo Fabrizio type kernel. A six chambered model with a single source of chlamydia is studied using the concept of fractal fractional derivatives with nonsingular and nonlocal fading memory. The fractal fractional model of the Chlamydia system can be solved by using the characteristics of a non-decreasing and compact mapping. Initially, we calculate the system’s equilibrium points and fundamental reproduction number R0. We then look at the system’s stability at the equilibrium point. Through the application of the Picard Lindelof methodology, we establish the existence of a unique solution for the given fractional CF-system of the hearing loss model and use fixed point theory to examine the stability of the iterative process. By taking into account the therapy as a control technique to lower the number of infected individuals, the system’s optimal control is established. Calculating the estimated solution of the system involves applying the Euler technique for the fractional order Caputo Fabrizio derivative. In two scenarios, R0 < 1 and R0 > 1, we provide a numerical simulation of the disease’s spread with regard to the basic reproduction number and the transmission rate. We compute the results for various fractional order derivatives and compare the findings in order to examine the impact of the fractional order derivative on the behavior and value of each variable in the model. Additionally, we examine the sensitivity of R0 with regard to each model parameter and ascertain the influence of each parameter, taking into account the significance of reproduction number in the persistence of disease transmission. Finally, it can be said that once more, fractional operator mathematical models can help in making better decisions on how to manage financially turbulent situations.
Dynamical transmission of Varicella Virus in Jordan with SVIR Model through analysis and numerical simulations
Chickenpox, another name for varicella virus, is a highly contagious illness. In this work, we use mathematical modelling and simulation to examine the dynamics of transmission and propose an SVIR model for the varicella virus in Jordan. The dynamics of the population in various classes are examined using a suggested model, which offers a more thorough comprehension of the course of the epidemic and the efficacy of control efforts. Lipschitz condition and fixed-point theory were also used to establish the solution's existence and uniqueness. Additionally, using figures and mathematics, it investigates the effects of different factors on the reproductive number and sensitivity analysis of the suggested model. The Routh-Hurwitz stability criterion is used to determine local stability at equilibrium sites that are both disease-free and endemic. Lyapunov functions with the first derivative test used to establish the global stability of model equilibria analysis for both >1 and <1. the suggested model is numerically simulated using Matlab software to ascertain how parameters affect the scenarios. The findings of this study confirm the theoretical and biological phenomena of the model and aid in elucidating the mechanisms of varicella virus transmission and directing public safety policy decisions. In the conclusion, Since the varicella virus puts a lot of demand on the country's healthcare system, the Jordanian Ministry of Health should launch vaccination campaigns in order to eliminate the disease because a universal varicella vaccination is necessary. Long-lasting protection from varicella immunization lowers the risk of epidemics and promotes community health, and lowering the overall burden of varicella virus infection frees up funds for other health concerns.
Mathematical Modeling of Covid-19 Model dynamical transmission with different way of infections
The COVID-19 pandemic is causing a lot of pain on a global scale. This work aims to develop new mathematical models for the outbreak by utilising fractional derivatives. Through the control of certain diseases, the adoption of changed methodologies and fundamental explanations can have a substantial impact on the fitness of society. Examining the dynamics and numerical approxima tions for the suggested arbitrary-order coronavirus illness system is the primary goal. For the Covid-19 model, the study introduces fractional derivatives using sophisticated methods such as the Atangana Baleanu, Sumudu transform, and Atangana-Toufik scheme. These methods yield accurate findings while examining the outbreak. Solutions involving various fractional operators are constructed using the Generalized Mittag-Leffler law. Covid-19 effects at various fractional values are explained and theoretical results are validated using numerical simulations. This aids in comprehending the outbreak and its management tactics.
Analysis of Energy Sector Model with Laplace Transform under modified fractional operator: Mathematical Analysis
Population growth is driving up energy demand, and burning fossil fuels accounts for a sizable amount of global energy production. Since this adds to the rise in greenhouse gas emissions, lowering energy sector emissions is essential to achieving climate change goals. In this research, three hybrid fractional operators are used to investigate carbon emissions from the power sector. A hy brid fractional operator is used to modify differential equations throughout time and space in order to create a mathematical model that describes the human population, energy consumption, and at mospheric carbon dioxide concentration. Compartmental models offer a mathematical framework for comprehending systems and forecasting outcomes, which makes them essential fgor comprehending real-world events. The effectiveness of these novel operators is supported by a number of analyses, and the Lipschitz condition ensures unique results. The order of the fractional derivative has a major impact on the dynamical process that is used to construct the non-integer order model.
Modeling and Stability Analysis of the Unemployment Model with Caputo
The problem of unemployment is acute, joblessness affects millions of people worldwide, which is why governments are constantly looking for efficient solutions to combat this social and economic ill. In response, we construct a model that encompasses the nonlinear nature of the unemployment rate. A fractional-order system of differential equations is employed in the structure of the considered model to produce a more accurate analysis of the unemployment dynamics of equilibrium positions and their stability or instability. In the model, there are three main dynamical parameters whose time evolution is described by fractional-order differential equations involving Caputo derivatives. The existence and uniqueness of the solutions are established by using the fixed point indices and the stability of the model is determined by applying the Hyers-Ulam stability test. A Newton polynomial approach is used for numerical simulation and investigates the results at fractional orders ω = 0.85 and ω = 1. The results presented in this paper suggest that there is one and only one stable positive equilibrium that is locally and globally asymptotically stable under some conditions. Computations demonstrate that for different values of ω, obtained with Caputo derivatives coinciding with the classical sense at ω = 1. In this study, by determining the employment rate and job creation rate that produce an unemployment rate of 7% the model complies with the governments policy objectives of low unemployment. These results provide important implications for the dynamic employment policies suggested and point to the use of fractional-order methodologies in other economic-social systems.
Analysis and Numerical Treatment of Chain Smokers using Advanced Fractional
In this paper, a fractal fractional derivative is used to examine an environmentally friendly approach of understanding the workings of smoking in humans. We proposed a fractional differential equation system to represent a time-fractional order smoking model with illness effects. Studies are conducted using methodologies. Lipschitz circumstances and linear growth are utilized to demonstrate the presence and distinction of the suggested model in relation to the impact of the global offset. It is confirmed that the fractional order model’s solutions are bounded and positive. When conducting the initial and subsequent derivative assessments, the Lyapunov function is employed to verify analysis of global stability. In order to examine the influence of smoking on humans, the fractional operator is studied. To do this, solutions are constructed applying the extended version of the Mittag-Leffler kernel using a two-step Lagrange polynomial method. Numerical simulation is performed to see how the fractional order smoking model behaves. Such research will aid in understanding the behavior of smoking and in developing human defenses.
Integral Transform and Generalized M-Series Fractional Integral Operators
This paper presents new theorems that build upon existing research by extending the ap plication of the Mellin transform within the framework of fractional integral operators. Traditionally, the Mellin transform has been a powerful tool for analyzing asymptotic behavior, scaling properties, and integral representations of special functions. However, by incorporating fractional integral oper ators, its analytical flexibility is significantly enhanced, allowing for a more in-depth study of special function properties, particularly in fractional calculus. Furthermore, the inclusion of the generalized I-function and M-series broadens this mathematical framework by generalizing established results and encompassing a wider class of special functions. Through their evaluation alongside fractional inte gral operators, this study introduces new integral representations, special cases, and applications that have not been previously explored. This extension greatly increases the applicability of these mathe matical tools in diverse fields such as mathematical physics, engineering, and applied analysis, where fractional calculus and integral transforms play a crucial role in solving complex differential equa tions and boundary value problems. Ultimately, these theorems not only refine existing mathematical structures but also create new opportunities for future research on the interplay between integral trans forms, special functions, and fractional calculus, contributing to both theoretical progress and practical advancements.
The primary objective of this research is to examine the model of Marburg virus disease with therapy to prevent the infections from spreading throughout the community due to saliva, urine, and feces. A mathematical model is established using the created hypothesis for a healthy environment in order to examine the different rates of Marburg virus disease after taking control measures with treatment for different protection. The model is then converted into a fractional ordered model for continuous monitoring, including theoretical solutions, by using the Fractal Fractional operator. The model’s global stability is studied through Lyapunov derivative by equilibrium and endemic point of model. Both qualitative and quantitative analysis is done on a proposed model with the power law kernel, with particular focus on unique solutions, positivity, and boundedness. By using of fixed point theory and the Lipschitz condition, there is only one exact solution. By confirming the Lyapunov function globally, equilibrium points that are both endemic and disease-free are checked for stability. Numerical simulations are utilized to investigate the effects of the fractal fractional operator on the generalized form of the power law kernel using a two-step Lagrange polynomial approach for ongoing monitoring of the Marburg virus disease and treatment strategies. The simulations show how different parameters affect the illness. In order to simulate the actual behavior and management of Marburg virus disease produced by saliva, urine, and feces and to implement control measures for a healthy environment with a hypersensitive reaction (HR), simulations have been constructed. This type of research will be helpful in figuring out how diseases spread and in developing management strategies based on our verified results for human in community.