Some Comprehensive Inequalities Consisting of Mittag-Leffler Type Functions in the Complex Plane

Abstract

Inequalities involving Mittag-Leffler functions play important roles in themselves and in their diverse applications. Many inequalities involving Mittag-Leffler functions have been established by a number of authors in many different ways. In this paper by making use of a novel idea and technique, a comprehensive result which contains several differential inequalities (in the complex plane ℂ) relating to the Mittag-Leffler (type) functions:(in its kernel (λ)v being the familier Pochhammer symbol) is first established. A number of corollaries and consequences of the main result are then presented.