Differential Equations and Dynamical Systems

, Volume 20, Issue 2, pp 139–148 | Cite as

Integro-Differential Equations of Fractional Order

Original Research
First Online:

Abstract

In this paper, the authors present some results concerning the existence and uniqueness of solutions of an integro-differential equation of fractional order by using Banach’s contraction principle, Schauder’s fixed point theorem, and the nonlinear alternative of Leray–Schauder type.

Keywords

Integro-differential equation Left-sided mixed Riemann–Liouville integral of fractional order Caputo fractional-order derivative, solution Banach’s contraction principle Schauder’s fixed point theorem Nonlinear alternative of Leray–Schauder type 

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2012

Authors and Affiliations

  • Saïd Abbas
    • 1
  • Mouffak Benchohra
    • 2
  • John R. Graef
    • 3
  1. 1.Laboratoire de MathématiquesUniversité de SaïdaSaïdaAlgeria
  2. 2.Laboratoire de MathématiquesUniversité de Sidi Bel-AbbèsSidi Bel-AbbesAlgeria
  3. 3.Department of MathematicsUniversity of Tennessee at ChattanoogaChattanoogaUSA

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