Compact and Noncompact Solutions to Generalized Sturm–Liouville and Langevin Equation with Caputo–Hadamard Fractional Derivative

Ahmed Salem, Noorah Mshary, Moustafa El-Shahed and Faris Alzahrani

Mathematical Problems in Engineering, 2021, vol. 2021, 1-15

Abstract:

In this work, through using the Caputo–Hadamard fractional derivative operator with three nonlocal Hadamard fractional integral boundary conditions, a new type of the fractional-order Sturm–Liouville and Langevin problem is introduced. The existence of solutions for this nonlinear boundary value problem is theoretically investigated based on the Krasnoselskii in the compact case and Darbo fixed point theorems in the noncompact case with aiding the Kuratowski’s measure of noncompactness. To demonstrate the applicability and validity of the main gained findings, some numerical examples are included.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:9995969

DOI: 10.1155/2021/9995969

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