Fractional differential equations with dependence on the Caputo-Katugampola derivative

Abstract

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

This is a preprint of a paper whose final and definite form is published in Journal of Computational and Nonlinear Dynamics

References in corpus (2)

• Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative
• Existence and Uniqueness results for a class of Generalized Fractional Differential Equations