Wavelet approximation scheme for distributed order fractional differential equations

This paper is concerned with the study of wavelet approximation scheme based on Legendre and Chebyshev wavelets for finding the approximate solutions of distributed order linear differential equations. The operational matrix for distributed order fractional differential operator is derived for Legendre and Chebyshev wavelets basis. Furthermore, the obtained operational matrix along with Gauss Legendre quadrature formula and standard Tau method are utilized to reduce the distributed order linear differential equations into the system of linear algebraic equations. For the better understanding of the method, numerical algorithms are also provided for the considered problems. In order to verify the desired accuracy of the proposed method, five test examples are included and numerical experiments confirm the theoretical results and illustrate applicability and efficiency of the proposed method. Also, the convergence analysis, error bounds, error estimate and numerical stability of presented method via Legendre and Chebyshev wavelets are investigated. Moreover, comparison of the numerical results obtained by the proposed approach is provided with the results of existing method. (C) 2020 Elsevier Ltd. All rights reserved.