Acta Applicandae Mathematicae

, Volume 109, Issue 3, pp 973–1033

A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions

  • Ravi P. Agarwal
  • Mouffak Benchohra
  • Samira Hamani

DOI: 10.1007/s10440-008-9356-6

Cite this article as:
Agarwal, R.P., Benchohra, M. & Hamani, S. Acta Appl Math (2010) 109: 973. doi:10.1007/s10440-008-9356-6


In this survey paper, we shall establish sufficient conditions for the existence and uniqueness of solutions for various classes of initial and boundary value problem for fractional differential equations and inclusions involving the Caputo fractional derivative. The both cases of convex and nonconvex valued right hand side are considered. The topological structure of the set of solutions is also considered.


Boundary value problem Initial value problems Differential equations and inclusions Caputo fractional derivative Fractional integral Existence Uniqueness Impulses Fixed point Selection Nonlocal conditions Integral conditions 

Mathematics Subject Classification (2000)

26A33 34A37 34A60 34B15 

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Ravi P. Agarwal
    • 1
  • Mouffak Benchohra
    • 2
  • Samira Hamani
    • 2
  1. 1.Department of Mathematical SciencesFlorida Institute of TechnologyMelbourneUSA
  2. 2.Laboratoire de MathématiquesUniversité de Sidi Bel-AbbèsSidi Bel-AbbèsAlgérie

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