Title: Expansion formula for generalised q-Mittag-Leffler function using Leibniz rule

Authors: Mulugeta Dawud Ali; Daya Lal Suthar

Addresses: Department of Mathematics, Wollo University, P.O. Box 1145, Dessie, Amhara, Ethiopia ' Department of Mathematics, Wollo University, P.O. Box 1145, Dessie, Amhara, Ethiopia

Abstract: In recent research, we have explored specific applications of the q-Leibniz rule. Through our investigations, we derived several intriguing transformations and expansions that involve various basic hypergeometric functions. These functions operate with one or more variables and include the fundamental analogue of Fox's H-function. This research papers explores novel expansion formulas that combine Fox's H-function with the generalised q-Mittag-Leffler function. By using the Leibniz rule to the q-Riemann and Weyl derivatives, these formulas derived more easily and open up new directions in mathematical analysis. Additionally, the study explores particular cases and uses arising from our primary finding, providing more context and understanding of the significance and usefulness of these expressions.

Keywords: q-Gamma function; q-Mittag-Leffler function; Leibniz rule; Riemann Liouville q-derivative; Weyl q-derivative.

DOI: 10.1504/IJANS.2024.146656

International Journal of Applied Nonlinear Science, 2024 Vol.4 No.4, pp.322 - 334

Received: 30 Sep 2024
Accepted: 23 Dec 2024

Published online: 11 Jun 2025 *

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