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Journal of Function Spaces
Volume 2017, Article ID 3046013, 8 pages
Research Article

Ulam Type Stability for a Coupled System of Boundary Value Problems of Nonlinear Fractional Differential Equations

1Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan
2Department of Mathematics, University of Malakand, Chakdara Dir (L), Khyber Pakhtunkhwa, Pakistan
3Department of Mathematics, Sun Yat-sen University, Guangzhou, China

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

Received 11 May 2017; Accepted 5 September 2017; Published 11 October 2017

Academic Editor: Hua Su

Copyright © 2017 Aziz Khan 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.


We discuss existence, uniqueness, and Hyers-Ulam stability of solutions for coupled nonlinear fractional order differential equations (FODEs) with boundary conditions. Using generalized metric space, we obtain some relaxed conditions for uniqueness of positive solutions for the mentioned problem by using Perov’s fixed point theorem. Moreover, necessary and sufficient conditions are obtained for existence of at least one solution by Leray-Schauder-type fixed point theorem. Further, we also develop some conditions for Hyers-Ulam stability. To demonstrate our main result, we provide a proper example.