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The Adomian decomposition method is proposed to solve fractional Bratu-type equations. The iteration procedure is based on a fractional Taylor series. Three examples are illustrated to show the presented method's efficiency and convenience.

In this paper, the modification of the homotopy perturbation method (MHPM) Zaid M. Odibat (Appl. Math. Comput. 2007) is extended to derive approximate solutions of the nonlinear coupled wave equations. This work will present a numerical comparison between the modification and the homotopy perturbation method (HPM). In order to show the ability and reliability of the method some examples are provided. The results reveal that the method is very effective and simple. The modified method accelerates the rapid convergence of the series solution and reduces the size of work.

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