Similarity Reductions, Power Series Solutions, and Conservation Laws of the Time-Fractional Mikhailov–Novikov–Wang System

Abstract

The current study presents a comprehensive Lie symmetry analysis for the time-fractional Mikhailov–Novikov–Wang (MNW) system with the Riemann–Liouville fractional derivative. The corresponding simplified equations with the Erdélyi–Kober fractional derivative are constructed by group invariant solutions. Furthermore, we obtain explicit solutions with the help of the power series method and show the dynamical behavior via evolutional figures. Finally, by means of Ibragimov’s new conservation theorem, the conservation laws are derived for the system.

Keywords

• fractional MNW system
• Lie symmetry analysis
• power series solutions
• conservation laws