Numerical implementation of nonlinear system of fractional Volterra integral–differential equations by Legendre wavelet method and error estimation

Abstract

AbstractIn the current study, a numerical scheme for solving the nonlinear system of fractional Volterra integro‐differential equations via Legendre wavelet is proposed. The Legendre wavelet operational matrix of fractional integration is derived and utilized to alter the main system to a system of algebraic equations. In addition, the error estimate of the original system is investigated in detail. Lastly, several numerical examples are set forth to test the proposed method and the obtained numerical results are compared with those from the CAS wavelet method.