Asymptotic Expansion of Solutions to the Dissipative Equation with Fractional Laplacian

2012 ◽  
Vol 44 (6) ◽  
pp. 3786-3805 ◽  
Author(s):  
Masakazu Yamamoto
Keyword(s):  
Asymptotic Expansion ◽  
Fractional Laplacian ◽  
Asymptotic Expansion Of Solutions ◽  
Dissipative Equation

scholarly journals Asymptotic Expansion of the Solutions to Time-Space Fractional Kuramoto-Sivashinsky Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Weishi Yin ◽  
Fei Xu ◽  
Weipeng Zhang ◽  
Yixian Gao
Keyword(s):  
Asymptotic Expansion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Initial Conditions ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Power Series Method ◽  
Time Space ◽  
Residual Power Series ◽  
Asymptotic Expansion Of Solutions

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.

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