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In this paper, based on the homotopy analysis method (HAM), a new analytic technique is proposed to solve non-linear Riccati differential equation with fractional order. Different from all other analytic methods, it provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter ℏ. Besides, it is proved that well-known Adomian’s decomposition...
In this paper, an analytic technique, namely the homotopy analysis method, is employed to solve the Fisher equation, which describes a family of travelling waves with a front. The explicit series solution for all possible wave speeds 0<c<+∞ is given. Such kind of explicit series solution has never been reported, to the best of author’s knowledge. Our series solution indicates that the solution...
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