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Laplace–Adomian decomposition method; Laplace-variational iteration method; reduced differential transform method; Lagrange multiplier; Caputo fractional derivative; Burgers’ equations

We solve the one- and two-dimensional fractional coupled Burgers’ equations (FCBEs) by three different methods. The proposed methods are the Laplace–Adomian decomposition method (LADM), the Laplace-variational iteration method (LVIM) and the reduced differential transform method (RDTM). The solutions are obtained as rapidly convergent series with simply calculable terms. Numerical studies of the application of theseapproaches for a number of sample problems are given and are illustrated graphically. With these methods, it is possible to investigate the nature of solutions when the fractional derivative parameters are changed. The numerical results reveal the effectiveness and the correctness of the proposed methods.

HODA F AHMED¹ M S M BAHGAT¹ MOFIDA ZAKI¹

1. Mathematics Department, Faculty of Science, El-Minia University, El-Minia, Egypt

Published

5 March 2019

Manuscript received

18 December 2017

Manuscript revised

7 July 2018

Accepted

11 July 2018

Early published

Unedited version published online

Final version published online

1 February 2019