LAUSR

In this paper, the Chebyshev–Gauss–Lobatto collocation method is developed for studying the variable-order (VO) time fractional model of the generalized Hirota–Satsuma coupled KdV system arising in interaction of long waves. To define this new system, the Atangana–Baleanu fractional operator is implemented. The operational matrix of VO fractional differentiation for the shifted Chebyshev polynomials is extracted and then, a collocation scheme is established to reduce the original VO fractional problem to a system of nonlinear algebraic equations. The validity of the presented method is investigated on two numerical examples.