Fractional differential equations with dependence on the Caputo-Katugampola derivative

摘要

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