A new generalization of Mittag-Leffler function via q -calculus

[摘要] The present paper deals with a new different generalization of the Mittag-Leffler function through q-calculus. We then investigate its remarkable properties like convergence, recurrence relation, integral representation, q-derivative formula, q-Laplace transformation, and image formula under q-derivative operator. In addition to this, we consider some specific cases to give the utilization of our main results.

[学科分类] 航空航天科学

[关键词] q -gamma functions;q -beta functions;Mittag-Leffler function