Space-time fractional Rosenou-Haynam equation: Lie symmetry analysis, explicit solutions and conservation laws

Abstract

This article uses the extension of the Lie symmetry analysis (LSA) and conservation laws (Cls) (Singla et al. in Nonlinear Dyn. 89(1):321-331, 2017; Singla et al. in J. Math. Phys. 58: 051503, 2017) for the space-time fractional partial differential equations (STFPDEs) to analyze the space-time fractional Rosenou-Haynam equation (STFRHE) with Riemann-Liouville (RL) derivative. We transform the space-time fractional RHE to a nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries. The reduced equation's derivative is in Erdelyi-Kober (EK) sense. We use the power series (PS) technique to derive explicit solutions for the reduced ODE for the first time. The Cls for the governing equation are constructed using a new conservation theorem.