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We prove the boundedness of the fractional integration operator of variable order α (x) in the limiting Sobolev case α (x) p (x) = n − λ (x) from variable exponent Morrey spaces L p ⋅ , λ ⋅ Ω into BMO (Ω), where Ω is a bounded open set. In the case α (x) ≡ const, we also show the boundedness from variable exponent vanishing Morrey spaces V L p ⋅ , λ ⋅ Ω into VMO (Ω). The results seem to be new even when p and λ are constant. [ABSTRACT FROM AUTHOR]

Abstract: Let , be a strongly Lipschitz domain in and a magnetic Schrödinger operator on satisfying the Dirichlet boundary condition, where and . In this paper, the authors introduce the Hardy space by the Lusin area function associated with and establish its equivalent characterization via the non-tangential maximal function associated with . As applications, the authors obtain the boundedness of the Riesz transforms , , from to for and the fractional integral from to for and , where is the closure of in . [Copyright &y& Elsevier]

Abstract: By using the coincidence degree theory due to Mawhin and constructing suitable operators, we study the existence of solutions to boundary value problems of fractional differential equations at resonance with . An example is given to illustrate our result. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we establish sufficient conditions for existence and uniqueness of solutions for some nondensely defined semilinear functional differential equations involving the Riemann–Liouville derivative. Our approach is based on integrated semigroup theory, the Banach contraction principle, and the nonlinear alternative of Leray–Schauder type. [Copyright &y& Elsevier]

Abstract: In this paper, we establish sufficient conditions for the existence of solutions for a class of boundary value problem for fractional differential equations involving the Caputo fractional derivative and nonlocal conditions. [Copyright &y& Elsevier]

Abstract: In this paper, we present fractional versions of the Filippov theorem and the Filippov–Wazewski theorem, as well as an existence result, compactness of the solution set and Hausdorff continuity of operator solutions for functional differential inclusions with fractional order, where is the standard Riemann–Liouville fractional derivative, and is a set-valued map. [Copyright &y& Elsevier]

Abstract: In this paper, we study fractional differential inclusions with Dirichlet boundary conditions. We prove the existence of a solution under both convexity and nonconvexity conditions on the multi-valued right-hand side. The proofs rely on nonlinear alternative Leray–Schauder type, Bressan–Colombo selection theorem and Covitz and Nadler’s fixed point theorem for multi-valued contractions. The compactness of the set solutions and relaxation results is also established. In the last section we consider the fractional boundary value problem with infinite delay. [Copyright &y& Elsevier]