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On nonlocal integral and derivative boundary value problem of nonlinear Hadamard Langevin equation with three different fractional orders

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Abstract

This paper is concerned with Hadamard fractional Langevin differential equation subject to fractional integral and derivative boundary conditions and which involves three different fractional orders. By using Schaefer’s fixed point theorem and Banach contraction principle, existence and uniqueness results of solutions for the proposed equation are obtained. An example demonstrating the consistency to the theoretical findings is also presented.

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Acknowledgements

The fourth author would like to thank Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) group number RG-DES-2017-01-17.

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Authors and Affiliations

  1. 08 May 1945 Guelma University, B.P. 401, 24000, Guelma, Algeria

    Amel Berhail & Nora Tabouche

  2. Department of Mathematics, Al-Azhar University-Gaza, Gaza, State of Palestine

    Mohammed M. Matar

  3. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia

    Jehad Alzabut

Authors
  1. Amel Berhail
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  2. Nora Tabouche
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  3. Mohammed M. Matar
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  4. Jehad Alzabut
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Correspondence to Jehad Alzabut.

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Berhail, A., Tabouche, N., Matar, M.M. et al. On nonlocal integral and derivative boundary value problem of nonlinear Hadamard Langevin equation with three different fractional orders. Bol. Soc. Mat. Mex. 26, 303–318 (2020). https://doi.org/10.1007/s40590-019-00257-z

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