Some relations involving a generalized fractional derivative operator

Abstract

Recently, Katugampola (Appl. Math. Comput. 218:860-865, 2011) studied a special case of the Erdélyi-Kober generalized fractional derivative. This special case generalized the well-known Riemann-Liouville and the Hadamard fractional integrals into a single form. Katugampola denoted this special case by the operator 0ρDxα. Some properties and examples for this fractional derivative operator was given. In this paper, we present some additional properties for this operator defined, this time, in the complex plane. In particular, we express this fractional derivative operator in terms of the classical Riemann-Liouville fractional derivative operator. A generalized Leibniz rule is obtained. © 2013 Gaboury et al.; licensee Springer.