On fractional differential inclusions with Nonlocal boundary conditions

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 {Dαu(t)+λDα−1u(t)∈F(t,u(t),Dα−1u(t)),t∈[0,1]Iβ0+u(t)|t=0=0,u(1)=Iγ0+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.