The main aim of the present work is to propose a new and simple algorithm for fractional
Zakharov–Kuznetsov equations by using homotopy perturbation transform method (HPTM). The Zakharov–Kuznetsov equation was first derived for describing weakly nonlinear ion-acoustic waves in strongly magnetized lossless plasma in two dimensions. The homotopy perturbation transform method is an innovative adjustment in Laplace transform algorithm (LTA) and makes the calculation much simpler. HPTM is not limited to the small parameter, such as in the classical perturbation method. The method gives an analytical solution in the form of a convergent
series with easily computable components, requiring no linearization or small perturbation.
The numerical solutions obtained by the proposed method indicate that the approach is easy to
implement and computationally very attractive.