On a Fractional Differential Inclusion in Banach Space Under Weak Compactness Condition

  • C. CastaingEmail author
  • C. Godet-Thobie
  • L. X. Truong
  • F. Z. Mostefai
Research Article
Part of the Advances in Mathematical Economics book series (MATHECON, volume 20)


We consider a class of boundary value problem in a separable Banach space governed by a fractional differential inclusion with integral boundary conditions
$$\displaystyle{\left \{\begin{array}{lll} w\text{-}D^{\alpha }u(t) \in F(t,u(t),w\text{-}D^{\alpha -1}u(t)), t \in [0,1] \\ I^{\beta }u(t)\vert _{t=0} = 0, u(1) =\int _{ 0}^{1}u(t)dt\end{array} \right.}$$
where α ∈ ]1, 2], \(\beta \in ]0,\infty [\) are given constant and w-D γ is the fractional w-R.L derivative of order γ ∈ {α − 1, α}, F is a convex weakly compact valued mapping. Topological properties of the solutions set are presented. Applications to control problems and further variants are provided.


Fractional differential inclusion w-R.L derivative Pettis integral Relaxation Young measures 


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Copyright information

© Springer Science+Business Media Singapore 2016

Authors and Affiliations

  • C. Castaing
    • 1
    Email author
  • C. Godet-Thobie
    • 2
  • L. X. Truong
    • 3
  • F. Z. Mostefai
    • 4
  1. 1.Département de MathématiquesUniversité Montpellier IIMontpellier Cedex 5France
  2. 2.Laboratoire de Mathématiques de Bretagne AtlantiqueUniversité de Bretagne Occidentale, CNRS UMR 6205Brest Cedex 3France
  3. 3.Department of Mathematics and StatisticsUniversity of Economics of HoChiMinh CityHoChiMinh CityVietnam
  4. 4.Département de MathématiquesUniversité de SaidaSaidaAlgérie

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