Application of cubic B-splines for second order fractional Sturm–Liouville problems

Arezu Aghazadeh and Mehrdad Lakestani

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 238, issue C, 479-496

Abstract: This paper presents a novel numerical method for determining the eigenvalues and eigenfunctions of a fractional second-order Sturm–Liouville problem, a model that represents a broad class of fractional-order differential equations commonly encountered in mathematical physics and engineering. The proposed approach combines cubic B-spline functions with the Galerkin method, transforming the problem into a system of algebraic equations. Additionally, operational matrices for fractional-order integrals and derivatives are constructed. The technique’s effectiveness and precision are illustrated through its application to various example problems.

Keywords: Sturm–Liouville eigenvalue problem; Caputo fractional derivative; Cubic B-spline (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:238:y:2025:i:c:p:479-496

DOI: 10.1016/j.matcom.2025.06.030

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