Compact and Noncompact Solutions to Generalized Sturm–Liouville and Langevin Equation with Caputo–Hadamard Fractional Derivative
| Autor: | Ahmed Salem, Faris Alzahrani, Noorah Mshary, Moustafa El-Shahed |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Article Subject
General Mathematics General Engineering Fixed-point theorem Sturm–Liouville theory Engineering (General). Civil engineering (General) Measure (mathematics) Fractional calculus Langevin equation Operator (computer programming) Hadamard transform QA1-939 Applied mathematics Boundary value problem TA1-2040 Mathematics |
| Zdroj: | Mathematical Problems in Engineering, Vol 2021 (2021) |
| ISSN: | 1024-123X |
| DOI: | 10.1155/2021/9995969 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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