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Boundary Value Problems for Nonlinear Implicit Caputo–Hadamard-Type Fractional Differential Equations with Impulses

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Abstract

In this paper, the authors establish the existence and uniqueness of solutions for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and Caputo–Hadamard type fractional derivatives. The stability of this problem is also studied. The arguments are based on the Banach contraction principle and Schaefer’s fixed point theorem. Two examples are presented to show the applicability of the results.

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Authors and Affiliations

  1. Laboratory of Mathematics, University of Sidi Bel-Abbes, P.O. Box 89 , 22000, Sidi Bel-Abbes, Algeria

    Mouffak Benchohra & Soufyane Bouriah

  2. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Mouffak Benchohra

  3. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN,  37403, USA

    John R. Graef

Authors
  1. Mouffak Benchohra
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  2. Soufyane Bouriah
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  3. John R. Graef
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Correspondence to John R. Graef.

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Benchohra, M., Bouriah, S. & Graef, J.R. Boundary Value Problems for Nonlinear Implicit Caputo–Hadamard-Type Fractional Differential Equations with Impulses. Mediterr. J. Math. 14, 206 (2017). https://doi.org/10.1007/s00009-017-1012-9

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  • DOI: https://doi.org/10.1007/s00009-017-1012-9

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