Exact Solutions and Conservation Laws of the Time-Fractional Gardner Equation with Time-Dependent Coefficients

Abstract

In this paper, we employ the certain theory of Lie symmetry analysis to discuss the time-fractional Gardner equation with time-dependent coefficients. The Lie point symmetry is applied to realize the symmetry reduction of the equation, and then the power series solutions in some specific cases are obtained. By virtue of the fractional conservation theorem, the conservation laws are constructed.

Keywords

• time-fractional Gardner equation
• Lie symmetry analysis
• power series solutions
• conservation laws