On a New Class of Hypergeometric Function

Abstract: The major objective of this article is to establish a new function called _pG^η_q,^ζ,m,ξ(z) which is generalization of the generalized hypergeometric function and Mittag-Leffler function and obtain its properties particular differential property, integral representation, derivative formula and some integral transform, Euler transform, Laplace transform, Whittaker transform. We also derived the relations that exist between _pG^η_q,^ζ,m,ξ(z) function with well known special functions. This article also deals with some fractional integral properties of the _pG^η_q,^ζ,m,ξ(z) function using the Riemann–Liouville fractional integrals and derivatives operators.