Extended Caputo fractional derivative operator

The principle aim of this paper is devoted to present an extended Caputo fractional derivative operator involving the generalized hyperge- ometric type function Fp(α,β;κ,μ) (a, b; c; z) introduced by Srivastava et al. and investigate some of its properties. In the sequel, extensions of some hypergeometric functions and their integral representations are also pre- sented by using the extended fractional derivative operator. Furthermore, linear and bilinear generating relations for the extended hypergeometric functions are obtained, and Mellin transforms of some extended hyperge- ometric functions and fractional derivatives are also determined.