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On generalized boundary value problems for a class of fractional differential inclusions. (English) Zbl 1391.34007

Summary: We prove existence of mild solutions to a class of semilinear fractional differential inclusions with non local conditions in a reflexive Banach space. We are able to avoid any kind of compactness assumptions both on the nonlinear term and on the semigroup generated by the linear part. We apply the obtained theoretical results to two diffusion models described by parabolic partial integro-differential inclusions.

MSC:

34A08 Fractional ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34G25 Evolution inclusions
35R11 Fractional partial differential equations
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