Fractional differential equations with dependence on the Caputo-Katugampola derivative

Ricardo Almeida; Agnieszka B. Malinowska; Tatiana Odzijewicz

Fractional differential equations with dependence on the Caputo-Katugampola derivative

Classical Analysis and ODEs 2016-07-26 v1

Authors: Ricardo Almeida , Agnieszka B. Malinowska , Tatiana Odzijewicz

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.

Keywords

fractional differential equation Caputo-Katugampola derivative fractional operator Cauchy type problem existence and uniqueness decomposition formula

Cite

@article{arxiv.1607.06913,
  title  = {Fractional differential equations with dependence on the Caputo-Katugampola derivative},
  author = {Ricardo Almeida and Agnieszka B. Malinowska and Tatiana Odzijewicz},
  journal= {arXiv preprint arXiv:1607.06913},
  year   = {2016}
}

Comments

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

Fractional differential equations with dependence on the Caputo-Katugampola derivative

Abstract

Keywords

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