Spectral technique for solving variable-order fractional Volterra integro-differential equations

Abstract

This article, presented a shifted Legendre Gauss-Lobatto collocation (SL-GL-C) method which is introduced for solving variable-order fractional Volterra integro-differential equation (VO-FVIDEs) subject to initial or nonlocal conditions. Based on shifted Legendre Gauss-Lobatto (SL-GL) quadrature, we treat with integral term in the aforementioned problems. Via the current approach, we convert such problem into a system of algebraic equations. After that we obtain the spectral solution directly for the proposed problem. The high accuracy of the method was proved by several illustrative examples.