Fractional Differential Equations With Dependence on the Caputo–Katugampola Derivative-Reference-Cited by-同舟云学术

Fractional Differential Equations With Dependence on the Caputo–Katugampola Derivative

Published:2016-09-16 Issue:6 Volume:11 Page:
ISSN:1555-1415
Container-title:Journal of Computational and Nonlinear Dynamics
language:en
Short-container-title:

Author:

Almeida Ricardo¹,Malinowska Agnieszka B.²,Odzijewicz Tatiana³

Affiliation:

1. Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Aveiro 3810–193, Portugal e-mail:

2. Faculty of Computer Science, Bialystok University of Technology, Białystok 15-351, Poland e-mail:

3. Department of Mathematics and Mathematical Economics, Warsaw School of Economics, Warsaw 02-554, Poland e-mail:

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 proved. 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 (FDE).

Publisher

ASME International

Subject

Applied Mathematics,Mechanical Engineering,Control and Systems Engineering,Applied Mathematics,Mechanical Engineering,Control and Systems Engineering

Link

http://asmedigitalcollection.asme.org/computationalnonlinear/article-pdf/doi/10.1115/1.4034432/6109595/cnd_011_06_061017.pdf

Reference21 articles.

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