Saker, M. A.Ezz-Eldien, S. S.Bhrawy, A. H.2019-12-232019-12-232017Cited References in Web of Science Core Collection: 561221-146Xhttps://cutt.ly/RreKK1GAccession Number: WOS:000396428400005In this paper, a new space-time spectral algorithm is constructed to solve the generalized Hirota-Satsuma coupled Korteweg-de Vries (GHS-C-KdV) system of time-fractional order. The present algorithm consists of applying the collocation-spectral method in conjunction with the operational matrix of fractional derivative for the double Jacobi polynomials, which will be employed as a basis function for the spectral solution. The main characteristic behind this approach is that such problems will reduce to those of solving algebraic systems of equations that greatly simplifying the problem. For ensuring the accuracy and efficiency of the presented algorithm, we apply it to find the approximate solutions of two specific problems, namely, a homogeneous form of the GHS-C-KdV system and a inhomogeneous GHS-C-KdV system.enOctober University for Generalized Hirota-Satsuma coupled KdV systemspectral colocation methodfractional Caputo derivativeoperational matrixJacobi-Gauss quadratureArticle