Combination of Lucas wavelets with Legendre-Gauss quadrature for fractional Fredholm-Volterra integro-differential equations

In this paper, the numerical technique with the help of the Lucas wavelets (LWs) and the Legendre-Gauss quadrature rule is presented to study the solution of fractional Fredholm-Volterra integro-differential equations. The modified operational matrices of integration and pseudo-operational of fractional derivative for the proposed wavelet functions are calculated. These matrices in comparison to operational matrices existing in other methods are more accurate. The Lucas wavelets and their operational matrices provide the precise numerical scheme to get the approximate solution. Also, we exhibit the upper bound of error based on the method. We illustrate the behavior of the new scheme in several numerical examples with the help of tables and figures. The results confirm the accuracy and applicability of the numerical approach. (C) 2020 Elsevier B.V. All rights reserved.