Asymptotic Expansion of the Solutions to Time‐Space Fractional Kuramoto‐Sivashinsky Equations

Weishi Yin, Fei Xu, Weipeng Zhang and Yixian Gao

Advances in Mathematical Physics, 2016, vol. 2016, issue 1

Abstract: This paper is devoted to finding the asymptotic expansion of solutions to fractional partial differential equations with initial conditions. A new method, the residual power series method, is proposed for time‐space fractional partial differential equations, where the fractional integral and derivative are described in the sense of Riemann‐Liouville integral and Caputo derivative. We apply the method to the linear and nonlinear time‐space fractional Kuramoto‐Sivashinsky equation with initial value and obtain asymptotic expansion of the solutions, which demonstrates the accuracy and efficiency of the method.

Date: 2016
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https://doi.org/10.1155/2016/4632163

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2016:y:2016:i:1:n:4632163

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