Lie symmetry analysis, conservation laws and explicit solutions for the time fractional Rosenau-Haynam equation

Under investigation in this paper is the invariance properties of the time-fractional Rosenau-Haynam equation, which can be used to describe the formation of patterns in liquid drops. Using the Lie group analysis method, the vector fields and symmetry reductions of the equation are derived, respectively. Moreover, based on the power series theory, a kind of explicit power series solutions for the equation is well constructed with a detailed derivation. The wave propagation pattern of these solutions are presented along the x axis with different t. Finally, using the new conservation theorem, two kinds of conservation laws of the equation are well constructed with a detailed derivation.