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Mittag-leffler-type function of arbitrary order and their application in the fractional kinetic equation

Author

Listed:
  • M. A. Pathan

    (Center for Mathematical and Statistical Sciences, KFRI)

  • Maged G. Bin-Saad

    (Aden University)

Abstract

In this paper, we stress the importance of the Mittag–Leffler function of two parameters and a single variable in the framework of mathematical physics and applied mathematics. We begin with pseudo hyperbolic and trigonometric functions and progress to introduce an arbitrary order Mittag–Leffler-type function. We study its properties, basic relations, integral representations, pure relations, and differential relations. We then justify the relevance of the arbitrary Mittag–Leffler-type function as a solution to the fractional kinetic equation. Also, we discuss the connection with known families of Mittag-Leffler functions and elementary functions and use operational tools to analyze all associated problems from a unified perspective.

Suggested Citation

  • M. A. Pathan & Maged G. Bin-Saad, 2023. "Mittag-leffler-type function of arbitrary order and their application in the fractional kinetic equation," Partial Differential Equations and Applications, Springer, vol. 4(2), pages 1-25, April.
    • Handle: RePEc:spr:pardea:v:4:y:2023:i:2:d:10.1007_s42985-023-00234-2
    DOI: 10.1007/s42985-023-00234-2
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    References listed on IDEAS

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    1. Francesco Mainardi & Armando Consiglio, 2020. "The Wright Functions of the Second Kind in Mathematical Physics," Mathematics, MDPI, vol. 8(6), pages 1-26, June.
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