Hadamard Functional Fractional Integrals and Derivatives and Fractional Differential Equations

Abstract

This paper introduces a general type  of new version of Hadamard  fractional integrals and  derivatives with respect to another function and studies some of their  properties. Further, we prove the existence results for fractional differential equations with this Hadamard type  fractional derivative. The results are obtained by using the Banach fixed point and the Schauder fixed point theorems. Examples are given to illustrate the theory.