Symmetry analysis, explicit power series solutions and conservation laws of the space-time fractional variant Boussinesq system

Abstract

In this study, the classical Lie symmetry method is successfully applied to investigate the symmetries of the space-time fractional variant Boussinesq system which was introduced as a model of water waves. With the help of the obtained symmetries, the governing system is reduced into the system of nonlinear fractional ordinary differential equations (NLFODEs) which contains Erdelyi-Kober fractional differential operators via Riemann-Liouville fractional derivative. The system is also studied for the explicit power series solution. The obtained power series solution is further examined for the convergence. The conservation laws of the governing system are constructed by using the new conservation theorem and generalization of the Noether operators. The numerical approximation for the fractional system is also found by using the residual power series method (RSPM). Some figures are also presented to explain the physical understanding for both explicit and approximate solutions.