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Abstract Boundary value problems involving ordinary differential equations arise in physical sciences and applied mathematics. In some of these problems, subsidiary conditions are imposed locally. In some other cases, nonlocal conditions are imposed. It is sometimes better to impose nonlocal conditions since the measurements needed by a nonlocal condition may be more precise than the measurement given by a local condition. Recently, the existence and the uniqueness of solutions of nonlocal problems have been studied by many authors using various methods. See, for example, ([6]-[7]), ([12]-[19]), ([22]-[28]), [40], ([46]-[49]), ([52]-[58]), [61], ([63]-[68]), ([70]-[74]), [79], [81] and ([86]-[88]). Fractional differential equations are generalizations of ordinary differential equations to an arbitrary (no integer) order. Fractional differential equations have attracted consid- erable interest because of their ability to model complex phenomena. These equations capture nonlocal relations in space and time with power-law memory kernels. Due to the extensive applications of FDEs in engineering and science, research in this area has grown significantly all around the world. |