Progress in Fractional Differentiation & Applications

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The aim of this paper is to demonstrate the extent to which the new iterative Sumudu transform method (NISTM) helps in solving three fractional KdV–Burgers equations (KdVB). In fact, new explanatory solutions are being obtained by using Caputo sense, which represents kernels power law type, Caputo–Fabrizio (CF) standing for exponentially with decaying type kernel and the Atangana–Baleanu (AB) representing the Mittag-Leffler type kernel. It is found that the model consisting of ABC fractional derivatives are affected more by the past than Caputo fractional derivative and CF fractional derivative. The accuracy and efficiency of the NISTM has been shown by studying the convergence of this technique.

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