Pseudospectral method for fourth-order fractional Sturm-Liouville problems

Haifa Bin Jebreen; Beatriz Hernández-Jiménez; Haifa Bin Jebreen; Beatriz Hernández-Jiménez

doi:10.3934/math.20241274

AIMS Mathematics

2024, Volume 9, Issue 9: 26077-26091. doi: 10.3934/math.20241274

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Pseudospectral method for fourth-order fractional Sturm-Liouville problems

Haifa Bin Jebreen ^{1
,
,},
Beatriz Hernández-Jiménez ²

1.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2.
Departamento de Economía, Métodos Cuantitativos e Historia Económica, Universidad Pablo de Olavide, 41013 Sevilla, Spain

Received: 19 June 2024 Revised: 19 July 2024 Accepted: 29 July 2024 Published: 09 September 2024
MSC : 34B24, 54A25, 65L60

Fourth-order fractional Sturm-Liouville problems are studied in this work. The numerical simulation uses the pseudospectral method, utilizing Chebyshev cardinal polynomials. The presented algorithm is implemented after converting the desired equation into an associated integral equation and gives us a linear system of algebraic equations. Then, we can find the eigenvalues by calculating the roots of the corresponding characteristic polynomial. What is most striking is that the proposed scheme accurately solves this type of equation. Numerical experiments confirm this claim.
- Chebyshev cardinal functions,
- fractional Sturm-Liouville problems,
- pseudospectral method
Citation: Haifa Bin Jebreen, Beatriz Hernández-Jiménez. Pseudospectral method for fourth-order fractional Sturm-Liouville problems[J]. AIMS Mathematics, 2024, 9(9): 26077-26091. doi: 10.3934/math.20241274

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Abstract

Fourth-order fractional Sturm-Liouville problems are studied in this work. The numerical simulation uses the pseudospectral method, utilizing Chebyshev cardinal polynomials. The presented algorithm is implemented after converting the desired equation into an associated integral equation and gives us a linear system of algebraic equations. Then, we can find the eigenvalues by calculating the roots of the corresponding characteristic polynomial. What is most striking is that the proposed scheme accurately solves this type of equation. Numerical experiments confirm this claim.

References

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