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Existence of Concave Positive Solutions for Nonlinear Fractional Differential Equation with p-Laplacian Operator

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Abstract

In this article, we investigate the existence and multiplicity of concave positive solutions for a boundary value problem for two-sided fractional differential equations involving the Caputo derivative. By means of the Leggett–Williams fixed point theorem, we obtain the existence of at least three solutions. Some illustrative examples are given in the last section.

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Authors and Affiliations

  1. Laboratoire de Mathématiques et Sciences appliquées, Université de Ghardaia, Ghardaia, Algeria

    Farid Chabane

  2. Department of Mathematics, University of Saïda–Dr. Moulay Tahar, P.O. Box 138, EN-Nasr, 20000, Saïda, Algeria

    Saïd Abbas

  3. Faculty of Sciences, Saad Dahlab University, Blida, Algeria

    Maamar Benbachir

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

    Mouffak Benchohra

  5. NEERLab, Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, M.D. 21252, USA

    Gaston N’Guérékata

Authors
  1. Farid Chabane
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  2. Saïd Abbas
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  3. Maamar Benbachir
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  4. Mouffak Benchohra
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  5. Gaston N’Guérékata
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Correspondence to Gaston N’Guérékata.

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Chabane, F., Abbas, S., Benbachir, M. et al. Existence of Concave Positive Solutions for Nonlinear Fractional Differential Equation with p-Laplacian Operator. Vietnam J. Math. 51, 505–543 (2023). https://doi.org/10.1007/s10013-022-00552-9

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  • DOI: https://doi.org/10.1007/s10013-022-00552-9

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