Applications of integral bifurcation method together with homogeneous balanced principle on investigating exact solutions of time fractional nonlinear PDEs

In this paper, it is verified that the fractional chain rule appeared in some references does not hold under Riemann–Liouville definition and Caputo definition of fractional derivative. It implies that this chain rule is invalid on searching exact solutions of fractional nonlinear partial differential equations (PDEs). Avoiding this chain rule, a new way of investigating exact solutions of fractional nonlinear PDEs is introduced. As examples, a series of time fractional nonlinear PDEs with diffusion and convection terms are studied. Different kinds of exact solutions of these equations are obtained, their dynamical properties are discussed, and the profiles of several representative exact solutions are illustrated.

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