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TOPOLOGICAL DEGREE METHOD FOR A \(\psi\)-HILFER FRACTIONAL DIFFERENTIAL EQUATION INVOLVING TWO DIFFERENT FRACTIONAL ORDERS

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Abstract

This paper investigates the existence and uniqueness of solution for a new class of \(\psi\)-Hilfer-type fractional differential equation with two fractional derivatives of different order. By making use of topological degree theory for condensing maps we established the existence result, for the reason that the previously mentioned theory softens the criteria of strong compactness by weakening it. To deal with the uniqueness result we use Banach’s contraction principle. As application, we give an example to demonstrate our theoretical result.

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Acknowledgements

The authors would like to thank the referees for the valuable comments and suggestions that improve the quality of our paper.

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Author notes

  1. Khalid Hilal and Ahmed Kajouni contributed equally to this work.

Authors and Affiliations

  1. Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco

    Hamid Lmou, Khalid Hilal & Ahmed Kajouni

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  1. Hamid Lmou
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  2. Khalid Hilal
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  3. Ahmed Kajouni
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Correspondence to Hamid Lmou.

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Lmou, H., Hilal, K. & Kajouni, A. TOPOLOGICAL DEGREE METHOD FOR A \(\psi\)-HILFER FRACTIONAL DIFFERENTIAL EQUATION INVOLVING TWO DIFFERENT FRACTIONAL ORDERS. J Math Sci 280, 212–223 (2024). https://doi.org/10.1007/s10958-023-06809-z

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