Unified Mittag-Leffler Function and Associated Integral Transforms and Fractional Integral Operators

Year 2025, Volume: 17 Issue: 2, 534 - 543, 30.12.2025

Muhammad Kaurangini , Umar Muhammad Abubakar , Enes Ata

https://doi.org/10.47000/tjmcs.1545292

Abstract

Unified Mittag-Leffler function defined by using beta function that consist of two Fox-Wright function in its kernel is introduced and its relation to Fox-Wright, Fox-$H$ functions and Mellin-Barnes type integral are illustrate. The beta, SUM, Laplace, Whittaker, $K$- and $P_{\partial}$- integral transforms are applied to the function and generalized formulas are obtained in form of both unified Mittag-Leffler and Fox-Wright functions. The convergence and differential formulas of this unified Mittag-Leffler function is also demonstrated.

Keywords

Mittag-Leffler function , Q Function , Fox-Wright function , SUM transform , Fox-H function , Laplace transform

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