A generalization of q-Mittag-Leffler Function with Four Parameters

Shaher  Momani; Shilpi  Jain; Rahul  Goyal; Praveen  Agarwal

doi:10.24996/ijs.2025.66.1.20

Authors

Shaher Momani Department, of Mathematics, The University of Jordan, Amman, Jordan / Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
Shilpi Jain Department of Mathematics, Poornima College of Engineering, Jaipur, India
Rahul Goyal Department of Mathematics, Anand International College of Engineering, Jaipur, India
Praveen Agarwal Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE / Department of Mathematics, Anand International College of Engineering, Jaipur, India https://orcid.org/0000-0001-7556-8942

DOI:

https://doi.org/10.24996/ijs.2025.66.1.20

Keywords:

Riemann Liouville fractional q-integral and derivative operator, Weyl-type fractional q-integral and derivative operator, Kober-type fractional q-integral and derivative operator, basic-analogue of Mittag-Leffler function, q-Laplace transform, q-Mellin transform

Abstract

The main purpose of this article is to introduce two different new basic analogue of the four parameters Mittag-Leffler function. Some q-integral representations and q-Mellin transforms for these q-analogues are derived. We have also obtained Riemann Liouville-type, Weyl-type and Kober-type fractional q-integrals and q-derivatives for these q-analogues of the four parameter Mittag-Leffler functions as the applications in q-fractional calculus.