Invariance properties, conservation laws, and soliton solutions of the time-fractional $$(2+1)$$ ( 2 + 1 ) -dimensional new coupled ZK system in magnetized dusty plasmas

Abstract

This paper investigates time-fractional $$(2+1)$$ -dimensional new coupled Zakharov–Kuznetsov system for the invariance properties, conservation laws, and soliton solutions. Lie infinitesimal symmetries and corresponding similarity reductions are carried out with Riemann–Liouville fractional derivative. The similarity reductions yield the reduced $$(1+1)$$ -dimensional nonlinear fractional partial differential equations having extended Erd $$\acute{\mathrm{e}}$$ lyi–Kober fractional differential operator. The new conservation theorem is used to determine the conserved vectors. The fractional complex transformation converts the given system into ordinary differential equations. Further more, the solutions of these ordinary differential equations are appeared in terms of bright, dark, and singular solitons. The graphical representation of solutions is presented to show the effect of fractional order $$\alpha $$ on the wave profile as well as on their velocity.