Legendre wavelet based numerical approach for solving a fractional eigenvalue problem

Abstract

A new method based on the Legendre wavelet is applied in the present work to deal with the numerical solution of the eigenvalue problem of the fractional differential equation. The eigenvalue problem is considered with a different class of boundary conditions. The exact fractional integration of the Legendre wavelet is used in the present work. The proposed scheme demonstrated to compute eigenvalues that are real as well as complex and to improve the eigenvalues by increasing the Legendre wavelet parameters. The eigenfunction corresponding to these eigenvalues is also calculated. The solution of the proposed scheme is also improved by increasing the order of the Legendre wavelet parameters. Moreover, this paper also investigates the convergence of the proposed approach through several examples. Numerical results show the efficiency and applicability of the proposed method for solving fractional eigenvalue problems.