Fractional differential equations with dependence on the Caputo-Katugampola derivative

摘要

In this paper we present a new type of fractional operator, the Caputo–Katugampoladerivative. The Caputo and the Caputo–Hadamard fractionalderivatives are special cases ofthis new operator. An existence and uniqueness theorem for afractional Cauchy type problem,with dependence on the Caputo–Katugampola derivative, is proven. A decomposition formulafor the Caputo–Katugampola derivative is obtained. This formula allows us to provide asimple numerical procedure to solve the fractional differential equation.