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- Title
Numerical method for solving fractional Sturm–Liouville eigenvalue problems of order two using Genocchi polynomials.
- Authors
Aghazadeh, A.; Mahmoudi, Y.; Saei, F. Dastmalchi
- Abstract
A new numerical scheme based on Genocchi polynomials is constructed to solve fractional Sturm–Liouville problems of order two in which the fractional derivative is considered in the Caputo sense. First, the differential equation with boundary conditions is converted into the corresponding integral equation form. Next, the fractional integration and derivation operational matrices for Genocchi polynomials, are introduced and applied for approximating the eigenvalues of the problem. Then, the proposed polynomials are applied to approximate the corresponding eigenfunctions. Finally, some examples are presented to illustrate the efficiency and accuracy of the numerical method. The results show that the proposed method is better than some other approximations involving orthogonal bases.
- Subjects
NUMERICAL solutions to Sturm-Liouville equations; EIGENVALUES; POLYNOMIALS; FRACTIONAL calculus; BOUNDARY value problems
- Publication
Iranian Journal of Numerical Analysis & Optimization, 2023, Vol 13, Issue 1, p121
- ISSN
2423-6977
- Publication type
Article
- DOI
10.22067/IJNAO.2022.75635.1115