Journal of Applied Mathematics and Computing

, Volume 53, Issue 1–2, pp 129–145 | Cite as

Existence of solutions for fractional differential equations with nonlocal and average type integral boundary conditions

  • Bashir AhmadEmail author
  • Sotiris K. Ntouyas
  • Ahmed Alsaedi
Original Research


In this paper, we establish sufficient conditions for the existence and uniqueness of solutions for a boundary value problem of fractional differential equations with nonlocal and average type integral boundary conditions. The Leray–Schauder nonlinear alternative, Krasnoselskii’s fixed point theorem and Banach’s fixed point theorem together with Hölder inequality are applied to construct proofs for the main results. Examples illustrating the obtained results are also presented.


Fractional differential equation Nonlocal Integral condition Existence and uniqueness Fixed point 

Mathematics Subject Classifications

34A08 34B10 



The authors thank the reviewers for their constructive remarks that led to the improvement of the original manuscript.


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Copyright information

© Korean Society for Computational and Applied Mathematics 2015

Authors and Affiliations

  • Bashir Ahmad
    • 1
    Email author
  • Sotiris K. Ntouyas
    • 1
    • 2
  • Ahmed Alsaedi
    • 1
  1. 1.Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Department of MathematicsUniversity of IoanninaIoanninaGreece

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