A wavelet-based novel technique for linear and nonlinear fractional Volterra–Fredholm integro-differential equations

In this paper, a wavelet-based operational matrix scheme has been introduced to obtain the approximate solution of the linear and nonlinear fractional order Volterra–Fredholm integro-differential equations. For the suggested approach, the operational matrix of the fractional integral for Taylor wavelets has been constructed. Then, the fractional integral operational matrix is utilized to reduce the solutions of linear and nonlinear Volterra–Fredholm integro-differential equations to systems of linear and nonlinear algebraic equations, respectively. Moreover, the convergence and error estimation of the proposed technique has been analyzed in this article. The numerical convergence rate is calculated to describe the accuracy of the presented method. Several illustrative experiments are included to verify the efficiency and validity of the proposed method. Also, the numerical results obtained by the suggested wavelet scheme have been compared with the other existing methods.