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

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

Shaher Momani
, Shilpi Jain
, Rahul Goyal
, Praveen Agarwal

Nonlinear Dynamic Research Centre (NDRC)

University of Jordan
Poornima College of Engineering
International College of Engineering

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Pages (from-to)	239-252
Number of pages	14
Journal	Iraqi Journal of Science
Volume	66
Issue number	1
DOIs	https://doi.org/10.24996/ijs.2025.66.1.20
State	Published - 2025

Keywords

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

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title = "A generalization of q-Mittag-Leffler Function with Four Parameters",

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.",

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

author = "Shaher Momani and Shilpi Jain and Rahul Goyal and Praveen Agarwal",

year = "2025",

doi = "10.24996/ijs.2025.66.1.20",

language = "English",

volume = "66",

pages = "239--252",

journal = "Iraqi Journal of Science",

issn = "0067-2904",

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TY - JOUR

T1 - A generalization of q-Mittag-Leffler Function with Four Parameters

AU - Momani, Shaher

AU - Jain, Shilpi

AU - Goyal, Rahul

AU - Agarwal, Praveen

PY - 2025

Y1 - 2025

N2 - 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.

AB - 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.

KW - Kober-type fractional q-integral and derivative operator

KW - Riemann Liouville fractional q-integral and derivative operator

KW - Weyl-type fractional q-integral and derivative operator

KW - basic-analogue of Mittag-Leffler function

KW - q-Laplace transform

KW - q-Mellin transform

UR - https://www.scopus.com/pages/publications/86000105507

U2 - 10.24996/ijs.2025.66.1.20

DO - 10.24996/ijs.2025.66.1.20

M3 - Article

AN - SCOPUS:86000105507

SN - 0067-2904

VL - 66

SP - 239

EP - 252

JO - Iraqi Journal of Science

JF - Iraqi Journal of Science

IS - 1

ER -

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

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Keywords

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