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

M. A. Pathan () and Maged G. Bin-Saad ()
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M. A. Pathan: Center for Mathematical and Statistical Sciences, KFRI
Maged G. Bin-Saad: Aden University

Partial Differential Equations and Applications, 2023, vol. 4, issue 2, 1-25

Abstract: 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.

Keywords: Mittag–Leffer function; Recurrence relations; Integral relations; Fractional kinetic equations; Lapla-ce transforms; 33C45; 33E12 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s42985-023-00234-2

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