Existence of periodic, solitary and compacton travelling wave solutions of a \((3+1)\)-dimensional time-fractional nonlinear evolution equations with applications (Q2222850)

The authors consider two nonlinear evolution equations with comfortable fractional derivatives in time: (1) a three-dimensional Wazwaz-Benjamin-Bona-Mahony equation; and (2) an energy-saving and emission-reduction system. By suitable transformations, the authors convert the fractional partial differential equations into ordinary differential equations. The bifurcation method is then applied to investigate the existence of periodic wave solutions, kink/anti-kink wave solutions, and solitary wave solutions.