Study of solitary and kink waves, stability analysis, and fractional effect in magnetized plasma

The (3 + 1)-dimensional fractional modified Zakharov Kuznetsov (mZK) equation is one of the nonlinear models to indicate the impact of magnetic fields on weak ion-acoustic waves in plasma; made up of cool and hot electrons. The primary goal of the present study is to use the (m + (G '))-expansion technique to seek the solutions G of mZK equation. The solutions are gained in the form of kink, dark, singular periodic and W-type soliton so-lutions. The influence of the fractional parameter on waveforms has also been examined by representing 2D and 3D graphs for distinct values of fractional-order beta. Moreover, we utilize Hamiltonian system properties to confirm the stability of the solution. The (m + (G '))-expansion technique can also be used to examine the nonlinear G evolution models being developed in various scientific and technological fields, such as mathematical physics and plasma physics. The soliton solutions attained by using the above technique have not been derived yet.