Author:
Castaing Charles,Godet-Thobie C.,Phung Phan D.,Truong Le X.
Abstract
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
$$\begin{array}{}
\displaystyle
\left\{ \begin{array}{lll} D ^\alpha u(t) +\lambda D^{\alpha-1 }u(t) \in F(t, u(t), D ^{\alpha-1}u(t)), \hskip 2pt t \in [0, 1] \\
I_{0^+}^{\beta }u(t)\left\vert _{t=0}\right. = 0, \quad u(1)=I_{0^+}^{\gamma }u(1)
\end{array}
\right.
\end{array}$$
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.
Subject
Applied Mathematics,Analysis
Reference70 articles.
1. Topologie de la convergence uniforme sur les parties uniformément intégrables de LE1$\begin{array}{} L^1_E \end{array}$ et théorèmes de compacité faible dans certains espaces du type Köthe-Orlicz;Sém. Anal. Convexe,1980
2. On a fractional differential inclusion with integral boundary conditions in Banach space;Fract. Calc. Appl. Anal.,2013
3. Measures of weak noncompactness in Banach spaces;Topology Appl.,2009
4. Fixed point theorem for weakly sequentially closed maps;Arch. Math. (Brno),2000
Cited by
15 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献