A matrix method for fractional Sturm-Liouville problems on bounded domain
Provides a numerical method for eigenvalue problems in fractional calculus, a niche domain-specific problem.
The paper proposes a matrix method for solving fractional Sturm-Liouville problems using Galerkin spectral methods with orthogonal polynomials, demonstrating convergence and competitiveness through numerical examples.
A matrix method for the solution of direct fractional Sturm-Liouville problems on bounded domain is proposed where the fractional derivative is defined in the Riesz sense. The scheme is based on the application of the Galerkin spectral method of orthogonal polynomials. The order of convergence of the eigenvalue approximations with respect to the matrix size is studied. Some numerical examples that confirm the theory and prove the competitiveness of the approach are finally presented.