On a coupled system of fractional differential equations with coupled nonlocal and integral boundary conditions |
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| Institution: | 1. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;2. Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece;1. Laboratory of Mathematics, University of Saïda, P.O. Box 138, Saïda 20000, Algeria;2. Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria;3. Faculty of Mathematics and Computational Science, Xiangtan University, Hunan 411105, PR China;4. Nonlinear Analysis and Applied Mathematics Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia |
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| Abstract: | We investigate a coupled system of fractional differential equations with nonlinearities depending on the unknown functions as well as their lower order fractional derivatives supplemented with coupled nonlocal and integral boundary conditions. We emphasize that the problem considered in the present setting is new and provides further insight into the study of nonlocal nonlinear coupled boundary value problems. We present two results in this paper: the first one dealing with the uniqueness of solutions for the given problem is established by applying contraction mapping principle, while the second one concerning the existence of solutions is obtained via Leray–Schauder’s alternative. The main results are well illustrated with the aid of examples. |
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