Numerical method for solving fractional Sturm–Liouville eigenvalue problems of order two using Genocchi polynomials

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 differen-tial equation with boundary conditions is converted into the corresponding integral equation form. Next, the fractional integration and derivation op-erational 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 accu-racy of the numerical method. The results show that the proposed method is better than some other approximations involving orthogonal bases.

Keywords

• sturm–liouville problem
• caputo fractional derivative
• eigen-value
• eigenfunction
• genocchi polynomials