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Initial value problem for hybrid \(\psi \)-Hilfer fractional implicit differential equations

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Abstract

This manuscript is devoted to proving the existence of solutions to a class of initial value problems for nonlinear fractional Hybrid implicit differential equations with a \(\psi \)-Hilfer fractional derivative. The result is based on a fixed point theorem due to Dhage. Examples are provided to demonstrate the result.

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Authors and Affiliations

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

    Abdelkrim Salim, Mouffak Benchohra & Jamal Eddine Lazreg

  2. 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

    Mouffak Benchohra

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

    John R. Graef

Authors
  1. Abdelkrim Salim
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  2. Mouffak Benchohra
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  3. John R. Graef
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  4. Jamal Eddine Lazreg
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Correspondence to John R. Graef.

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Salim, A., Benchohra, M., Graef, J.R. et al. Initial value problem for hybrid \(\psi \)-Hilfer fractional implicit differential equations. J. Fixed Point Theory Appl. 24, 7 (2022). https://doi.org/10.1007/s11784-021-00920-x

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  • DOI: https://doi.org/10.1007/s11784-021-00920-x

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