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.