Further extended Caputo fractional derivative operator and its applications

In this paper, our principle aim is to establish a new extension of the Caputo fractional derivative operator involving the generalized hypergeometric type function Fp(a, b; c; z; k), introduced by Lee et al. Some extensions of the generalized hypergeometric functions and their integral representations are also presented. Furthermore, linear and bilinear generating relations for the extended hypergeometric functions are obtained. We also present some properties of the extended fractional derivative operator.