Abstract

The main purpose of this paper is to study a class of boundary value problem governed by a fractional differential inclusion in a separable Banach space E { D α u ( t ) + λ D α − 1 u ( t ) ∈ F ( t , u ( t ) , D α − 1 u ( t ) ) , t ∈ [ 0 , 1 ] I β 0 + u ( t ) | t = 0 = 0 , u ( 1 ) = I γ 0 + u ( 1 ) in both Bochner and Pettis settings, where α ∈ ]1, 2], β ∈ [0, 2 – α], λ ≥ 0, γ > 0 are given constants, Dα is the standard Riemann-Liouville fractional derivative, and F : [0, 1] × E × E → 2E is a closed valued multifunction. Topological properties of the solution set are presented. Applications to control problems and subdifferential operators are provided.