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Complexity
Volume 2017 (2017), Article ID 7676814, 9 pages
https://doi.org/10.1155/2017/7676814
Research Article

Application of Topological Degree Method for Solutions of Coupled Systems of Multipoints Boundary Value Problems of Fractional Order Hybrid Differential Equations

1Department of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhwa, Pakistan
2Department of Mathematics, Sun Yat-Sen University, Guangzhou, China

Correspondence should be addressed to Yongjin Li; nc.ude.usys.liam@jylsts

Received 15 March 2017; Revised 26 April 2017; Accepted 11 May 2017; Published 20 July 2017

Academic Editor: Sundarapandian Vaidyanathan

Copyright © 2017 Muhammad Iqbal et al. 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

We established the theory to coupled systems of multipoints boundary value problems of fractional order hybrid differential equations with nonlinear perturbations of second type involving Caputo fractional derivative. The proposed problem is as follows: , , , , , , , , , where , is linear, is Caputo fractional derivative of order , with , , and is fractional integral of order . The nonlinear functions , are continuous. For obtaining sufficient conditions on existence and uniqueness of positive solutions to the above system, we used the technique of topological degree theory. Finally, we illustrated the main results by a concrete example.