Some results for fractional boundary value problem of differential inclusions

  • Ouahab A
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Abstract

In this paper, we study fractional differential inclusions with Dirichlet boundary conditions. We prove the existence of a solution under both convexity and nonconvexity conditions on the multi-valued right-hand side. The proofs rely on nonlinear alternative Leray-Schauder type, Bressan-Colombo selection theorem and Covitz and Nadler's fixed point theorem for multi-valued contractions. The compactness of the set solutions and relaxation results is also established. In the last section we consider the fractional boundary value problem with infinite delay. © 2007 Elsevier Ltd. All rights reserved.

Author-supplied keywords

  • Boundary
  • Compactness
  • Continuous selection
  • Decomposable
  • Fixed point
  • Fractional derivative
  • Fractional differential inclusions
  • Fractional integral
  • Functional differential inclusions
  • Infinite delay
  • Relaxation theorem

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