Some Properties of a Generalized Mittag-Leffler Type Function

This paper is concerned to the study of a new generalized function of Mittag-Leffler type. Its various properties including Laplace transform, Beta transform, Mellin transform, Whittaker transform, generalized hypergeometric series form, Mellin-Barnes integral representation and its relationship with Fox's H-function and Wright hypergeometric function are established. Also derived the relations that exist between this function and the operators of Riemann-Liouville fractional integrals and derivatives. These presentations make the reader familiar with the present trend of research in Mittag-Leffler functions and their applications.