Lie Symmetry Analysis and Explicit Solutions for the Time-Fractional Regularized Long-Wave Equation

This paper systematically investigates the Lie group analysis method of time-fractional regularized long-wave (RLW) equation with Riemann–Liouville fractional derivative. The vector fields and similarity reductions are obtained. It is shown that governing can be transformed into a ordinary differential new independent variable, where derivatives in Erdèlyi–Kober sense. Furthermore, explicit analytic solutions obtained using power series expansion method. Finally, some graphical features were presented to give visual interpretation solutions.