This paper focuses on the asymptotic solutions to time-space fractional coupled systems, where the fractional derivative and integral are described in the sense of Caputo derivative and Riemann-Liouville integral. We introduce the Residual Power Series (for short RPS) method to construct the desired asymptotic solutions. Furthermore, we apply this method to some time-space fractional coupled systems. The simplicity and efficiency of RPS method are shown by the application.
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