The Existence of Solutions for an Initial Value Problem of Caputo-katugampola Fractional Differential Equations

In this paper, the existence and uniqueness results of solution for an initial value problem of fractional differential equations with a new concept of fractional derivative in the case of the order α ϵ (1,2) have been investigated. This concept is based on the Caputo fractional derivative and Caputo-Hadamard fractional derivative into a single form. Banach's contraction mapping principle is used to obtain the existence and uniqueness results..