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A Study on k-Generalized ψ-Hilfer Derivative Operator

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Abstract

In this paper, we generalize the ψ-Hilfer fractional derivative and discuss some of its properties. We prove existence, uniqueness and stability results for a class of initial value problems for implicit nonlinear fractional differential equations involving generalized ψ-Hilfer fractional derivative. The uniqueness result for the given problem is obtained via the Banach contraction mapping principle. In addition, two examples are given to illustrate our results.

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Acknowledgements

The work of Juan J. Nieto has been partially supported by the Agencia Estatal de Investigación (AEI) of Spain, co-financed by the European Fund for Regional Development (FEDER) corresponding to the 2014-2020 multiyear financial framework, project MTM2016-75140-P and by Xunta de Galicia under grant ED431C 2019/02. We thank the reviewers for their useful remarks on our work.

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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, Jamal Eddine Lazreg & Mouffak Benchohra

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

    Bashir Ahmad & Mouffak Benchohra

  3. Departamento de Estatistica, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Spain

    Juan J. Nieto

Authors
  1. Abdelkrim Salim
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  2. Jamal Eddine Lazreg
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  3. Bashir Ahmad
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  4. Mouffak Benchohra
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  5. Juan J. Nieto
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Correspondence to Bashir Ahmad.

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Salim, A., Lazreg, J.E., Ahmad, B. et al. A Study on k-Generalized ψ-Hilfer Derivative Operator. Vietnam J. Math. 52, 25–43 (2024). https://doi.org/10.1007/s10013-022-00561-8

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  • DOI: https://doi.org/10.1007/s10013-022-00561-8

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