The major objective of this article is to establish a new function called pGη,ζ,m,ξ q (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 pGη,ζ,m,ξ q (z) function with well known special functions. This article also deals with some fractional integral properties of the pGη,ζ,m,ξ q (z) function using the Riemann– Liouville fractional integrals and derivatives operators.
hypergeometric functions, Mittag-Leffler functions, Riemann– Liouville fractional integral and derivatives