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New Fractional Derivatives Applied to the Korteweg-De Vries and Korteweg-De Vries-Burger's Equations

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2018

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Springer Heidelberg

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Abstract

In 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.

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Time Fractional Korteweg-De Vries, Time Fractional Korteweg-De Vries-Burger's, Q-Homotopy Analysis Transform Method, Liouville-Caputo, Caputo-Fabrizio, Atangana-Baleanu

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Saad, 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)

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Computational & Applied Mathematics

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37

Issue

4

Start Page

5203

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5216