A Quantum Generalized Mittag-Leffler Function Via Caputo q-Fractional Equations

TL;DR

This paper introduces a new q-analogue of the Mittag-Leffler function via Caputo q-fractional difference equations and demonstrates its use in solving such equations using successive approximation.

Contribution

It presents a novel generalized q-Mittag-Leffler function and applies it to solve Caputo q-fractional difference equations, extending previous work by Kilbas and Saigo.

Findings

Solutions expressed with the new q-Mittag-Leffler function

Method of successive approximation applied successfully

Extension of classical Mittag-Leffler functions to q-calculus

Abstract

Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions. The obtained q-version of Mittag-Leffler function is thought as the q-analogue of the one introduced previously by Kilbas and Saigo.