Some Fractional Calculus Operators Associated with Generalized Mittag-Leffler Funcitons

Authors

  • Santosh Verma Department of Mathematics,Guru Ghasidas Vishwavidyalaya A Central University, Bilaspur - 495009, India

DOI:

https://doi.org/10.48165/jmmfc.2025.2203

Keywords:

Saigo Integral operators, Mittag-Leffler functions.

Abstract

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.

References

Chaurasia, V. B. L., and S. C. Pandey. “On the new computable solution of the generalized frac tional kinetic equations involving the generalized function for the fractional calculus and related functions.”Astrophysics and space science 317 (2008): 213-219.

Erdlyi, Arthur. “Higher transcendental functions.”Higher transcendental functions (1953): 59.

Scalas, Enrico, Rudolf Gorenflo, and Francesco Mainardi. “Fractional calculus and continuous time finance.”Physica A: Statistical Mechanics and its Applications 284.1-4 (2000): 376-384.

Kilbas, Anatoli Aleksandrovich, Hari M. Srivastava, and Juan J. Trujillo. Theory and applications of fractional differential equations. Vol. 204. elsevier, 2006.

Kilbas, Anatoly A., Megumi Saigo, and Ram K. Saxena. “Generalized Mittag-Leffler function and generalized fractional calculus operators.”Integral Transforms and Special Functions 15.1 (2004): 31-49.

Kilbasi, Anatoly A., and Megumi Saigo. “On Mittag-Leffler type function, fractional calculas op erators and solutions of integral equations.”Integral Transforms and Special Functions 4.4 (1996): 355-370.

Hilfer, Rudolf, ed. Applications of fractional calculus in physics. World scientific, 2000.

Prabhakar, Tilak Raj. “A singular integral equation with a generalized Mittag Leffler function in the kernel.”Yokohama Mathematical Journa 19.1 (1971): 7-15.

Salim, Tariq O. “Some properties relating to the generalized Mittag-Leffler function.”Adv. Appl. Math. Anal 4.1 (2009): 21-30.

Saigo, Megumi. “A remark on integral operators involving the Gauss hypergeometric func tions.”(1978): 135-143.

Saigo, Megumi. “A certain boundary value problem for the Euler-Darboux equation. II.”Vol.25 (1980).

Saigo, M., R. K. Saxena, and J. Ram. “On the fractional calculus operator associated with the H-function.”Ganita Sandesh 6.1 (1992): 36-47.

Saxena, R. K., A. M. Mathai, and H. J. Haubold. “Fractional reaction-diffusion equa tions.”Astrophysics and space science 305 (2006): 289-296.

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Published

2026-02-03

How to Cite

Some Fractional Calculus Operators Associated with Generalized Mittag-Leffler Funcitons. (2026). Journal of Mathematical Modeling and Fractional Calculus, 2(2), 30-37. https://doi.org/10.48165/jmmfc.2025.2203