Some Properties of Generalized Mittag-Leffler Type Function Via q-Calculus

Abstract

In this paper, we introduce a new generalization of the Mittag-Leffler function, called the q-analogue of the generalized Mittag-Leffler type function, and investigate its interesting and useful properties such as the condition of convergence, recurrence relations, differential formulae, integral representation, and images of this function under the q-Laplace and q-Sumudu transforms. Some interesting special cases of the main finding are also addressed and demonstrated to be related to some well-known ones.