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A Generalized Lyapunov Inequality for a Pantograph Boundary Value Problem Involving a Variable Order Hadamard Fractional Derivative

Author

Listed:
  • John R. Graef

    (Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37401, USA)

  • Kadda Maazouz

    (Department of Mathematics, University of Ibn Khaldoun, Tiaret P.O. Box 78, Algeria)

  • Moussa Daif Allah Zaak

    (Department of Mathematics, University of Ibn Khaldoun, Tiaret P.O. Box 78, Algeria)

Abstract

The authors obtain existence and uniqueness results for a nonlinear fractional pantograph boundary value problem containing a variable order Hadamard fractional derivative. This type of model is appropriate for applications involving processes that occur in strongly anomalous media. They also derive a generalized Lyapunov-type inequality for the problem considered. Their results are obtained by the fractional calculus and Krasnosel’skii’s fixed point theorem. An example is given to illustrate their approach.

Suggested Citation

  • John R. Graef & Kadda Maazouz & Moussa Daif Allah Zaak, 2023. "A Generalized Lyapunov Inequality for a Pantograph Boundary Value Problem Involving a Variable Order Hadamard Fractional Derivative," Mathematics, MDPI, vol. 11(13), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2984-:d:1186541
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    References listed on IDEAS

    as
    1. Almeida, Ricardo & Torres, Delfim F.M., 2015. "Computing Hadamard type operators of variable fractional order," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 74-88.
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