Lie Symmetries, Conservation Laws and Explicit Solutions for Time Fractional Rosenau–Haynam Equation**Supported by the Fundamental Research Fund for Talents Cultivation Project of the China University of Mining and Technology under Grant No. YC150003

Abstract

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. By 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 are well constructed with a detailed derivation. Finally, by using the new conservation theorem, two kinds of conservation laws of the equation are well constructed with a detailed derivation.