Applications of homogenous balanced principle on investigating exact solutions to a series of time fractional nonlinear PDEs

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• 作者：Weiguo Rui ^{weiguorhhu@aliyun.com wgruihhu@163.com}
• 关键词：Nonlinear time fractional PDEs ; Homogenous balanced principle ; Function-expansion method of separation variables ; Mittag&ndash ; Leffler function ; Fractional chain rule
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：2017
• 出版时间：June 2017
• 年：2017
• 卷：47
• 期：Complete
• 页码：253-266
• 全文大小：2870 K
• 卷排序：47

文摘

By using a counterexample, the fractional chain rule appeared in many references has been proved that it does not hold under Riemann–Liouville definition and Caputo definition of fractional derivative. This implies that this chain rule is invalid in investigating exact solutions of nonlinear fractional partial differential equations (PDEs). In order to seek exact solutions of nonlinear time fractional PDEs, the function-expansion method of separation variable type based on the homogenous balanced principle is introduced. By using this method, a series of nonlinear time fractional PDEs are studied. Their exact solutions are obtained and dynamical properties of these exact solutions are discussed.