Ulam Type Stability for a Coupled System of Boundary Value Problems of Nonlinear Fractional Differential Equations. (11th October 2017) - Khan, Aziz; Shah, Kamal; Li, Yongjin; Khan, Tahir Saeed
Abstract : 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.