Time fractional (2+1)-dimensional Wu–Zhang system: Dispersion analysis, similarity reductions, conservation laws, and exact solutions

This paper examines the time fractional (2+1)-dimensional Wu–Zhang system describing dispersive long waves. The dispersion relation of waves has been obtained from linear analysis and used to find the phase and group velocity. The dispersion relation shows an anomalous dispersion of waves. Lie symmetries and the corresponding similarity reductions are carried out using Riemann–Liouville fractional derivative and the order of the system is reduced to lower dimension. Furthermore, the system is analysed for nonlinear self-adjointness and the conservation laws are obtained associated with infinitesimal symmetries by applying new conservation theorem. The adjoint variables are used to convert conservation laws into original dependent variables. The exponential rational function method is employed to find exact solutions revealing kink and bell type profiles. The effect of fractional order α on the wave profile of solutions is discussed graphically.