A Study of k-generalized Mittag-Leffler Type Function with Four Parameters

Abstract

This study introduces a new generalization of the Mittag-Leffler function, the k-generalized Mittag-Leffler type function , , , ( ), γ δ α β E z k and investigates its interesting and important basic properties, such as useful relationships between Mittag-Leffler functions, recurrence relations, differential formulas, integral representations, and images of this function under the Euler (Beta), Laplace, and Whittaker transforms. Some interesting special cases of the main finding are also addressed and demonstrated to be related to some well-known ones.