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Fractional Calculus and Applied Analysis

, Volume 16, Issue 3, pp 538–558 | Cite as

On a fractional differential inclusion with integral boundary conditions in Banach space

  • Phan Dinh Phung
  • Le Xuan Truong
Research Paper
  • 115 Downloads

Abstract

We consider a class of boundary value problem in a separable Banach space E, involving a nonlinear differential inclusion of fractional order with integral boundary conditions, of the form
$$\left\{ \begin{gathered} D^\alpha u(t) \in F(t,u(t),D^{\alpha - 1} u(t)),a.e.,t \in [0,1], \hfill \\ I^\beta u(t)|_{t = 0} = 0,u(1) = \int\limits_0^1 {u(t)dt,} \hfill \\ \end{gathered} \right. $$
(*)
where D α is the standard Riemann-Liouville fractional derivative, F is a closed valued mapping. Under suitable conditions we prove that the solutions set of (*) is nonempty and is a retract in W E α,1 (I). An application in control theory is also provided by using the Young measures.

Key Words and Phrases

fractional differential inclusion boundary value problem Green’s function contractive set valued-map retract Young measures 

MSC 2010

26A33 34A60 34B10 34A08 47N70 

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Copyright information

© Versita Warsaw and Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.Nguyen Tat Thanh UniversityHoChiMinh CityVietnam
  2. 2.Department of Mathematics and StatisticsUniversity of Economics HoChiMinh CityHoChiMinh CityVietnam

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