Saad, Khaled M.Baleanu, DumitruAtangana, Abdon2020-03-262020-03-262018Saad, Khaled M.; Baleanu, Dumitru; Atangana, Abdon, "New fractional derivatives applied to the Korteweg-de Vries and Korteweg-de Vries-Burger's equations", Computational & Applied Mathematics. Vol. 37, No 4, pp. 5203,5216, (2018)0101-8205http://hdl.handle.net/20.500.12416/2743In this paper, we extend the model of the Korteweg-de Vries (KDV) and Korteweg-de Vries-Burger's (KDVB) to new model time fractional Korteweg-de Vries (TFKDV) and time fractional Korteweg-de Vries-Burger's (TFKDVB) with Liouville-Caputo (LC), Caputo-Fabrizio (CF), and Atangana-Baleanu (AB) fractional time derivative equations, respectively. We utilize the q-homotopy analysis transform method (q-HATM) to compute the approximate solutions of TFKDV and TFKDVB using LC, CF and AB in Liouville-Caputo sense. We study the convergence analysis of q-HATM by computing the Residual Error Function (REF) and finding the interval of the convergence through the h-curves. Also, we find the optimal values of h so that, we assure the convergence of the approximate solutions. The results are very effective and accurate in solving the TFKDV and TFKDVB.eninfo:eu-repo/semantics/closedAccessTime Fractional Korteweg-De VriesTime Fractional Korteweg-De Vries-Burger'sQ-Homotopy Analysis Transform MethodLiouville-CaputoCaputo-FabrizioAtangana-BaleanuArticle3745203521610.1007/s40314-018-0627-1