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

作者：Rui, Weiguo^*

来源：Communications in Nonlinear Science & Numerical Simulation, 2017, 47: 253-266.

DOI：10.1016/j.cnsns.2016.11.018

• Nonlinear time fractional PDEs
• Homogenous balanced principle
• Function-expansion method of separation
• variables
• Mittag-Leffler function
• Fractional chain rule

By using a counterexample, we proved the fractional chain rule appeared in many references does not hold under Riemann-Liouville definition and Caputo definition of fractional derivative. It shows that this chain rule is invalid in investigating exact solutions of nonlinear fractional partial differential equations (PDEs). In this paper, based on the homogenous balanced principle, the function-expansion method of separation variable type are introduced. By using this method, a series of nonlinear time fractional PDEs such as time fractional KdV equation and Burgers equation, time fractional diffusion-convection equations are studied from mathematical viewpoint. The dynamical properties of these exact solutions are discussed and the profiles of several representative exact solutions are illustrated.

• 出版日期2017-6
• 单位重庆师范大学