Abstract
In this paper, we study a coupled system of Caputo type fractional differential equations with integral boundary conditions. By Leray-Schauder alternative theorem, the existence of solutions for the factional differential system are obtained. The Hyers-Ulam stability of solutions is discussed and sufficient conditions for the stability are developed. The main results are well illustrated with examples and numerical simulation graphs. The interesting point of this article is that it not only gives approximate graphs of solution by using the iterative methods, but also verifies the Hyers-Ulam stability of the coupling system by numerical simulation.
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