Abstract: A generalized auxiliary equation method, which combines fractional complex transform with [(G/G)]-expansion method, is extended to systematically construct exact solutions of nonlinear space-time fractional differential equations with the aid of computerized symbolic computation software Mathematica in a natural way. The method is used to obtain the exact solutions of fractional Calogero KDV equation. The method provides a promising tool for finding exact solutions of fractional nonlinear partial differential equations.

Key words: [(G/G)]-expansion method, modified Riemann-Liouville derivative, fractional Calogero KDV equation

摘要： 将分数阶复变换方法和[(G/G)]方法相结合得到了一种辅助方程方法，用来求解分数阶非线性微分方程。利用该方法并借助于软件Mathematica的符号计算功能求解了分数阶Calogero KDV方程，得到了该方程新的精确解。

关键词: [(G/G)]-方法, 修正Riemann-Liouville导数, 分数阶Calogero KDV方程