Author Guidelines

Journal of Mathematical Modeling and Fractional Calculus

The Journal of Mathematical Modeling and Fractional Calculus (JMMFC) publishes high-quality original research that advances mathematical modeling, fractional calculus, differential equations, dynamical systems, numerical analysis, computational mathematics, and their applications to real-world scientific and engineering problems.

Authors are requested to carefully read these guidelines before submitting their manuscripts.

1. Scope of the Journal

Manuscripts submitted to JMMFC should fall within the aims and scope of the journal. The journal welcomes original theoretical, computational, and applied research in areas including, but not limited to:

  • Mathematical modeling of scientific, engineering, biological, medical, environmental, and social systems

  • Fractional calculus and fractional differential equations

  • Integer-order and fractional-order differential equations

  • Ordinary and partial differential equations

  • Fractional derivatives and integral operators

  • Mathematical analysis and qualitative theory

  • Dynamical systems and stability analysis

  • Bifurcation and chaos theory

  • Numerical and computational methods

  • Analytical and approximate solutions

  • Integral transforms and special functions

  • Control theory and optimal control

  • Mathematical epidemiology and population dynamics

  • Mathematical models in biology and medicine

  • Fluid dynamics, heat and mass transfer modeling

  • Mathematical physics and engineering applications

  • Novel mathematical methods, algorithms, and their applications

Manuscripts must demonstrate a clear mathematical contribution, originality, scientific significance, and relevance to the journal's scope.

2. Types of Manuscripts

The journal considers the following categories of manuscripts:

Original Research Articles

Original theoretical, analytical, computational, or applied research presenting new and significant findings.

Review Articles

Comprehensive and critical reviews of important and emerging areas of mathematical modeling or fractional calculus.

Short Communications

Brief reports presenting important new mathematical results, methods, or applications.

Authors submitting review articles are encouraged to contact the Editorial Office before submission.

3. General Manuscript Requirements

Manuscripts must:

  • Be original and unpublished.

  • Not be under consideration for publication elsewhere.

  • Be written in clear and professional English.

  • Present scientifically and mathematically sound results.

  • Clearly identify the novelty and contribution of the research.

  • Include appropriate references to relevant previous literature.

  • Follow accepted standards of research ethics and publication integrity.

The corresponding author is responsible for ensuring that all authors have approved the submitted manuscript and agree with its content.

4. Manuscript Preparation

Authors should submit their manuscripts in Microsoft Word (.doc or .docx) format.

For manuscripts containing extensive mathematical equations, authors may also provide the source file in LaTeX format, where applicable.

The manuscript should be arranged in the following order:

  1. Title

  2. Author name(s)

  3. Author affiliation(s)

  4. Corresponding author details

  5. Abstract

  6. Keywords

  7. Introduction

  8. Mathematical formulation / Methodology

  9. Results and Discussion

  10. Conclusions

  11. Acknowledgements

  12. Funding Information

  13. Conflict of Interest

  14. Data Availability Statement

  15. References

The structure may be modified where necessary according to the nature of the mathematical research.

5. Title

The title should:

  • Be concise and informative.

  • Clearly reflect the main subject of the research.

  • Avoid unnecessary abbreviations.

  • Indicate the mathematical model, method, or application where appropriate.

Example:

Stability and Numerical Analysis of a Fractional-Order Epidemic Model with Vaccination

6. Author Names and Affiliations

The manuscript should include:

  • Full name of each author

  • Department

  • Institution or University

  • City and Country

  • Email address of the corresponding author

Clearly identify the corresponding author using an asterisk (*).

Example:

Author Name¹*, Author Name²

¹ Department of Mathematics, University Name, City, Country
² Department of Applied Mathematics, Institution Name, City, Country

Corresponding Author: email@example.com

7. Abstract

The abstract should provide a concise summary of the research.

It should generally include:

  • Background or research problem

  • Objective of the study

  • Mathematical method or model used

  • Main theoretical or numerical findings

  • Major conclusions and significance

The abstract should normally be 150–250 words and should be understandable without referring to the main text.

Avoid citations, undefined abbreviations, and excessively complex mathematical expressions in the abstract.

8. Keywords

Provide 4–8 keywords immediately after the abstract.

Keywords should be specific and useful for indexing and discovery.

Example:

Fractional calculus; Mathematical modeling; Stability analysis; Caputo derivative; Numerical simulation; Dynamical systems.

9. Introduction

The Introduction should:

  • Clearly describe the research problem.

  • Provide relevant background literature.

  • Explain the importance of the study.

  • Identify limitations or gaps in previous research.

  • Clearly state the novelty and objectives of the work.

Authors should clearly distinguish their contribution from previously published studies.

10. Mathematical Formulation and Methodology

The mathematical model or methodology should be presented clearly and systematically.

Authors should:

  • Define all variables and parameters.

  • Clearly state assumptions.

  • Provide the governing equations.

  • Define initial and boundary conditions where applicable.

  • Explain the choice of fractional derivative or operator.

  • Describe analytical, numerical, or computational methods used.

  • Provide sufficient detail to allow verification or reproduction of the results.

All mathematical symbols should be consistently defined.

11. Mathematical Equations

Equations should be clearly formatted and numbered consecutively where necessary.

Example:

Dtαx(t)=f(x,t),0<α≤1D_t^\alpha x(t)=f(x,t), \quad 0<\alpha\leq1

All symbols appearing in equations must be properly explained in the text.

Authors should avoid using images or screenshots for mathematical equations whenever editable equations can be provided.

12. Results and Discussion

Results should be presented clearly and supported by appropriate mathematical analysis, numerical computations, tables, or figures.

The discussion should:

  • Interpret the mathematical results.

  • Explain their theoretical or practical significance.

  • Compare findings with relevant previous studies where appropriate.

  • Clearly discuss the limitations of the proposed model or method.

Numerical simulations must include sufficient information about computational methods, parameter values, software, and algorithms used.

13. Tables

Tables should:

  • Be numbered consecutively.

  • Have a clear and descriptive title.

  • Be cited in the text.

  • Be submitted in editable format.

  • Avoid duplication of information already presented in figures.

Example:

Table 1. Model parameters and their descriptions.

14. Figures and Graphs

Figures should be:

  • Numbered consecutively.

  • Clearly cited in the manuscript.

  • Accompanied by informative captions.

  • Of high quality and readable resolution.

Graphs should include clearly labeled axes, units where applicable, and appropriate legends.

Authors should ensure that all figures remain clear and readable after publication.

15. Numerical Results and Simulations

For manuscripts involving numerical methods or simulations, authors should provide sufficient details regarding:

  • Numerical scheme or algorithm

  • Software or programming language used

  • Computational parameters

  • Initial and boundary conditions

  • Parameter values

  • Error analysis or convergence analysis, where applicable

Results should be reproducible as far as reasonably possible.

16. Conclusions

The conclusion should clearly summarize:

  • The major findings.

  • The mathematical contribution of the research.

  • The practical or theoretical significance of the results.

  • Possible directions for future research.

The conclusion should not merely repeat the abstract.

17. Acknowledgements

Authors may acknowledge individuals, institutions, technical assistance, or organizations that contributed to the research but do not meet the criteria for authorship.

18. Funding Information

Authors should clearly disclose all sources of financial support.

Example:

Funding: This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

19. Conflict of Interest

All authors must disclose any financial or non-financial conflicts of interest.

Example:

Conflict of Interest: The authors declare that they have no conflict of interest.

20. Data and Code Availability

Authors are encouraged to provide information regarding the availability of data, computational code, algorithms, or supplementary material.

Example:

Data Availability: The data supporting the findings of this study are available from the corresponding author upon reasonable request.

For computational studies, authors are encouraged to make relevant codes or algorithms available whenever possible.

21. References

References should be relevant, accurate, and carefully checked.

Authors must ensure that:

  • Every reference cited in the text appears in the reference list.

  • Every reference in the reference list is cited in the text.

  • Author names, journal titles, volume, issue, page numbers, and DOI information are accurate.

  • References are directly relevant to the research.

Authors should give appropriate recognition to foundational and recent literature in the field.

Where available, authors are encouraged to include the DOI for cited publications.

22. Originality and Plagiarism

Submitted manuscripts must be original work.

The journal does not accept:

  • Plagiarized manuscripts.

  • Substantially duplicated publications.

  • Previously published manuscripts presented as new work.

  • Simultaneous submissions to multiple journals.

  • Manipulation or fabrication of research results.

All manuscripts may be screened for similarity and publication ethics issues before or during the peer-review process.

Authors are responsible for ensuring the originality of their work and proper citation of previously published material.

23. Artificial Intelligence (AI) Tools

The use of artificial intelligence tools for language assistance, coding assistance, data processing, or other research support should be disclosed where such use materially contributes to the manuscript.

AI tools cannot be listed as authors because authorship requires responsibility and accountability for the published work.

Authors remain fully responsible for:

  • The accuracy of all content.

  • Mathematical calculations and results.

  • Citations and references.

  • Originality of the manuscript.

  • Any material generated or assisted by AI tools.

24. Authorship

Authorship should be limited to individuals who have made substantial contributions to the research.

All authors must:

  • Approve the final version of the manuscript.

  • Agree to its submission to the journal.

  • Accept responsibility for their contribution to the work.

The corresponding author is responsible for communication with the journal throughout the submission, review, and publication process.

25. Peer Review Process

All suitable manuscripts undergo editorial screening to determine whether they fall within the scope of the journal and meet the required scientific and technical standards.

Manuscripts that pass the initial screening are sent for peer review.

Editorial decisions may include:

  • Accept

  • Minor Revision

  • Major Revision

  • Reject

Acceptance for publication is based on originality, mathematical quality, scientific validity, clarity, relevance, and the recommendations of reviewers and editors.

26. Article Processing Charges

Information regarding publication charges, if applicable, will be communicated according to the journal's current publication policy.

Authors should note that submission and initial editorial evaluation are subject to the journal's applicable policies. Any publication charges, where applicable, are communicated in accordance with the journal's procedures.

27. Copyright and Open Access

The Journal of Mathematical Modeling and Fractional Calculus follows the applicable ACS Publisher publishing and open-access policies.

Authors should review the journal's current copyright, licensing, and publication policies before submission.

28. Submission Checklist

Before submitting a manuscript, authors should confirm that:

☐ The manuscript is within the scope of JMMFC.
☐ The manuscript is original and has not been published previously.
☐ The manuscript is not under consideration by another journal.
☐ All authors have approved the submitted version.
☐ The title accurately reflects the research.
☐ The abstract clearly summarizes the study.
☐ Appropriate keywords have been provided.
☐ All mathematical symbols and variables are properly defined.
☐ Equations are clearly formatted and editable.
☐ Tables and figures are properly numbered and cited.
☐ References have been carefully checked.
☐ Funding information has been disclosed.
☐ Conflicts of interest have been declared.
☐ Data or code availability information has been provided where applicable.

29. Submission

Authors should submit their manuscripts through the journal's online submission system.

Submit a Manuscript to JMMFC

For general submission assistance, authors may also contact the ACS Publisher Editorial Office through the official publisher channels.

Important Note

Submission of a manuscript to the Journal of Mathematical Modeling and Fractional Calculus confirms that the authors have read and agreed to the journal's editorial, ethical, and publication requirements.