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

John R. Graef (), Kadda Maazouz and Moussa Daif Allah Zaak
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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

Mathematics, 2023, vol. 11, issue 13, 1-16

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.

Keywords: Lyapunov inequality; variable order fractional operators; Krasnosel’skii’s fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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