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New fractional derivatives with non-singular kernel applied to the Burgers equation. (English) Zbl 1394.35565

Summary: In this paper, we extend the model of the Burgers (B) to the new model of time fractional Burgers (TFB) based on Liouville-Caputo (LC), Caputo-Fabrizio (CF), and Mittag-Leffler (ML) fractional time derivatives, respectively. We utilize the Homotopy Analysis Transform Method (HATM) to compute the approximate solutions of TFB using LC, CF, and ML in the Liouville-Caputo sense. We study the convergence analysis of HATM by computing the interval of the convergence, the residual error function (REF), and the average residual error (ARE), respectively. The results are very effective and accurate.{
©2018 American Institute of Physics}

MSC:

35R11 Fractional partial differential equations
35Q53 KdV equations (Korteweg-de Vries equations)
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