Jacobi–Gauss–Lobatto collocation approach for non-singular variable-order time fractional generalized Kuramoto–Sivashinsky equation

This paper introduces the non-singular variable-order (VO) time fractional version of the generalized Kuramoto–Sivashinsky (GKS) equation with the aid of fractional differentiation in the Caputo–Fabrizio sense. The Jacobi–Gauss–Lobatto collocation technique is developed for solving this equation. More precisely, the derivative matrix of the classical Jacobi polynomials and the VO fractional derivative matrix of the shifted Jacobi polynomials (which is obtained in this study) together with the collocation technique are used to transform the solution of problem into the solution of an algebraic system of equations. Numerical simulations for several test problems have been shown to accredit the established algorithm.