LAUSR

The article is devoted in the study of the Kadomtsev–Petviashvili modified equal width equation with fractional temporal evolution in which modified Riemann–Liouville derivative is considered. We discuss the dynamical behavior of the system using bifurcation theory in different parametric regions. We also depict the phase portraits of the traveling wave solutions and obtain explicit traveling waves including solitary wave and breaking wave solution. We apply the $$(G'/G)$$(G′/G)-expansion method and the F-expansion method along with fractional complex transformation, and obtain a large variety of exact traveling wave solutions which includes solitary wave, kink-type wave, and periodic wave solutions of the equation. Finally, we demonstrate remarkable features of the traveling wave solutions via interesting figures and phase portraits.