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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 174156, 9 pages
http://dx.doi.org/10.1155/2015/174156
Research Article

On the Nonlinear Fractional Differential Equations with Caputo Sequential Fractional Derivative

1School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
2School of Mathematics, South China University of Technology, Guangzhou 510641, China

Received 3 August 2015; Accepted 27 October 2015

Academic Editor: Ivan Avramidi

Copyright © 2015 Hailong Ye and Rui Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The purpose of this paper is to investigate the existence of solutions to the following initial value problem for nonlinear fractional differential equation involving Caputo sequential fractional derivative , , , , where , are Caputo fractional derivatives, , , , and . Local existence of solutions is established by employing Schauder fixed point theorem. Then a growth condition imposed to guarantees not only the global existence of solutions on the interval , but also the fact that the intervals of existence of solutions with any fixed initial value can be extended to . Three illustrative examples are also presented. Existence results for initial value problems of ordinary differential equations with -Laplacian on the half-axis follow as a special case of our results.