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

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Abstract

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.

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Acknowledgments

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

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Authors and Affiliations

  1. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Bashir Ahmad, Sotiris K. Ntouyas & Ahmed Alsaedi

  2. Department of Mathematics, University of Ioannina, 451 10, Ioannina, Greece

    Sotiris K. Ntouyas

Authors
  1. Bashir Ahmad
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  2. Sotiris K. Ntouyas
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  3. Ahmed Alsaedi
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Correspondence to Bashir Ahmad.

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Ahmad, B., Ntouyas, S.K. & Alsaedi, A. Existence of solutions for fractional differential equations with nonlocal and average type integral boundary conditions. J. Appl. Math. Comput. 53, 129–145 (2017). https://doi.org/10.1007/s12190-015-0960-0

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  • DOI: https://doi.org/10.1007/s12190-015-0960-0

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