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Some boundary value problems of fractional differential equations and inclusions. (English) Zbl 1228.34011

Summary: We study the existence of solutions for nonlinear fractional differential equations and inclusions of order \(q\in (1,2]\) with families of mixed and closed boundary conditions. In case of inclusion problems, the existence results are established for convex as well as nonconvex multivalued maps. Our results are based on Leray-Schauder degree theory, nonlinear alternative of Leray-Schauder type, and some fixed point theorems for multivalued maps. Some interesting special cases are also discussed.

MSC:

34A08 Fractional ordinary differential equations
47H10 Fixed-point theorems
34B99 Boundary value problems for ordinary differential equations
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