Approximate Solutions of the Fractional Zakharov-Kuznetsov Equation Using Laplace-Residual Power Series Method

An analytical solution is proposed in this work for the non-linear time-fractional Zakharov-Kuznetsov partial differential equation (FZK-PDE) in the Caputo sense. The FZK-PDE model demonstrates the behavior of weakly nonlinear ion-acoustic waves in a plasma with a uniform magnetic field. A series solution for the FZK-PDE is obtained using the so-called Laplace-Residual power series method (L-RPSM). The L-RPSM is a simple and efficient technique for obtaining approximate and exact series solution of nonlinear and linear fractional differential equations (FDEs). Graphical and numerical solutions of several test examples show the reliability and efficiency of the L-RPSM. Moreover, the results show that the L-RPSM is powerful, competitive, simple, and reliable for a wide range of fractional PDEs.