Some new results for multi-valued fractional evolution equations

Rong-Nian Wang and Qing-Hua Ma

Applied Mathematics and Computation, 2015, vol. 257, issue C, 285-294

Abstract: Given a closed linear operator A in a Banach space X and a multi-valued function with convex, closed values F:[0,b]×C([-τ,0];X)→2X, we consider the Cauchy problemcDtαu(t)∈Au(t)+F(t,ut),t∈[0,b],u(t)=φ(t),t∈[-τ,0],where τ⩾0,cDtα,0<α<1, represents the regularized Caputo fractional derivative of order α. We concentrate on the case when the semigroup generated by A is noncompact and obtain nonemptyness of the solution set if, in particular, X is reflexive and F is weakly upper semicontinuous with respect to the second variable. Furthermore, in this situation topological properties of the set of all solutions are considered.

Keywords: Fractional evolution inclusion; Solvability; Topological properties of the solution set; Weakly upper semicontinuity (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:257:y:2015:i:c:p:285-294

DOI: 10.1016/j.amc.2014.08.035

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