In this article, the new approach called, the optimal auxiliary function method (OAFM) has been extended with the help of the fractional complex transform method (FCTM) to fractional order partial differential equations (PDEs). The beauty of the method is that, there is no need for small or large parameter assumption in the problem. Similarly, the proposed method gives an approximate solution after only one itearion. To test the proposed method, we take the time-fractional order Zakharov-Kuznetsov equations as a test example. The computed results of the suggested method are compared with the new iterative method (NIM), perturbation iteration method (PIA), and Residual power series method (RPSM). The accuracy and effectiveness of the proposed method can be proven by numerical and graphical results.

在本文中，借助于分数复数变换方法（FCTM）将称为最佳辅助函数方法（OAFM）的新方法扩展为分数阶偏微分方程（PDE）。该方法的优点在于，在此问题中无需大大小小的参数假设。类似地，所提出的方法仅在一次迭代后就给出了近似解。为了测试所提出的方法，我们以时间分数阶的Zakharov-Kuznetsov方程为例。将该方法的计算结果与新的迭代方法（NIM），扰动迭代方法（PIA）和残差幂级数方法（RPSM）进行了比较。数值和图形结果可以证明所提方法的准确性和有效性。