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A Study of Fractional Differential Equations and Inclusions with Nonlocal Erdélyi–Kober Type Integral Boundary Conditions

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Abstract

In this paper, we study a new kind of nonlocal boundary value problems of nonlinear fractional differential equations supplemented with Erdélyi–Kober type fractional integral conditions. The uniqueness of solutions for the given problem is established by means of contraction map** principle. Applying nonlinear alternative for contractive maps, we investigate the inclusions case of the problem at hand. Examples illustrating the main results are constructed as well.

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Acknowledgements

The authors thank the reviewers for their useful comments that led to the improvement of the original manuscript. This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia under grant no. (KEP-MSc-10-130-39). The authors, therefore, acknowledge with thanks DSR technical and financial support.

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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, Yong Zhou & Ahmed Alsaedi

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

    Sotiris K. Ntouyas

  3. Faculty of Mathematics and Computational Science, **angtan University, Hunan, People’s Republic of China

    Yong Zhou

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

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Communicated by Asadollah Aghajani.

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Ahmad, B., Ntouyas, S.K., Zhou, Y. et al. A Study of Fractional Differential Equations and Inclusions with Nonlocal Erdélyi–Kober Type Integral Boundary Conditions. Bull. Iran. Math. Soc. 44, 1315–1328 (2018). https://doi.org/10.1007/s41980-018-0093-y

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  • DOI: https://doi.org/10.1007/s41980-018-0093-y

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