Sahand Communications in Mathematical Analysis

Exploring Fractional $q$-Kinetic Equations via Generalized $q$-Mittag-Leffler Type Functions: Applications and Analysis

Document Type : Research Paper

Authors

Mulugeta Dawud Ali 1
Dayalal Suthar 1
Sunil Dutt Purohit 2

1 Department of Mathematics, College of Natural Science, Wollo University, P.O. Box 1145, Dessie, Ethiopia.

2 Department of HEAS (Mathematics), Rajasthan Technical University, Kota, Rajasthan, India.

https://doi.org/10.22130/scma.2025.2063077.2211
Abstract
In this study, the $q$-calculus is employed to introduce a novel generalization of the Mittag-Leffler function. In the following, we investigate a novel $q$-exponential function with five parameters, resulting in the generalized $q$-Mittag-Leffler function.  Some $q$-integral representations and fractional $q$-derivative (Caputo  and Hilfer) for this $q$-Mittag-Leffler type function are derived. Moreover, we obtain the solutions to the $q$-fractional kinetic equations includes this function by applying $q$-Laplace and $q$-Sumudu transforms defined using fractional $q$-calculus operators of the Riemann-Liouville (R-L) type. A few particular scenarios to illustrate the use of our primary finding. Further, we state some significant and special cases of our main results. Finally, we present the obtained solutions in the form of numerical graphs using MATLAB 16.

Keywords

q-Mittag-Leffler function
q-Laplace transform
q-Beta function
q-Gamma function
Fractional q-calculus operator

Subjects

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Sahand Communications in Mathematical Analysis
Volume 23, Issue 1
Winter 2026
Pages 161-183

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