Pseudospectral method for solving fractional Sturm-Liouville problem using Chebyshev cardinal functions

Abstract

This work deals with the pseudospectral method to solve the Sturm-Liouville eigenvalue problems with Caputo fractional derivative using Chebyshev cardinal functions. The method is based on reducing the problem to a weakly singular Volterra integrodifferential equation. Then, using the matrices obtained from the representation of the fractional integration operator and derivative operator based on Chebyshev cardinal functions, the equation becomes an algebraic system. To get the eigenvalues, we find the roots of the characteristics polynomial of the coefficients matrix. We have proved the convergence of the proposed method. To illustrate the ability and accuracy of the method, some numerical examples are presented.