By the framework of power function for studying exact solutions of time-fractional CH-γ equation

Compared to solving integer-order nonlinear partial differential equations, solving fractional-order nonlinear partial differential equations is significantly more challenging. In this paper, based on the separation method of semi-fixed variables, by using a power function as the framework for solving nonlinear time-fractional partial differential equations. The time-fractional CH-γ equation is reduced to a higher-order ordinary differential system and then uses the phase portrait analysis of dynamical systems to investigate the exact solutions and dynamic properties of the time-fractional CH-γ equation. Under specific parameter conditions, various exact solutions of the time-fractional CH-γ equation are obtained, and the dynamic behavior of some solutions is intuitively illustrated through three-dimensional graphs which show their evolution behavior in time and space dimensions.