Zada Laiq, Nawaz Rashid, Jamshed Wasim, Ibrahim Rabha W, Tag El Din El Sayed M, Raizah Zehba, Amjad Ayesha
Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khyber Pakhtunkhwa, 23200, Pakistan.
Department of Mathematics, Capital University of Science and Technology (CUST), Islamabad, 44000, Pakistan.
Sci Rep. 2022 Nov 6;12(1):18838. doi: 10.1038/s41598-022-23644-5.
The second iteration of the optimal homotopy asymptotic technique (OHAM-2) has been protracted to fractional order partial differential equations in this work for the first time (FPDEs). Without any transformation, the suggested approach can be used to solve fractional-order nonlinear Zakharov-Kuznetsov equations. The Caputo notion of the fractional-order derivative, whose values fall within the closed interval [0, 1], has been taken into consideration. The method's appeal is that it provides an approximate solution after just one iteration. The suggested method's numerical findings have been contrasted with those of the variational iteration method, residual power series method, and perturbation iteration method. Through tables and graphs, the proposed method's effectiveness and dependability are demonstrated.
本文首次将最优同伦渐近技术的第二次迭代（OHAM - 2）扩展应用于分数阶偏微分方程（FPDEs）。无需任何变换，所提出的方法可用于求解分数阶非线性扎哈罗夫 - 库兹涅佐夫方程。已考虑分数阶导数的卡普托定义，其值落在闭区间[0, 1]内。该方法的优点是仅经过一次迭代就能提供近似解。所提方法的数值结果已与变分迭代法、残差幂级数法和摄动迭代法的结果进行了对比。通过表格和图形展示了所提方法的有效性和可靠性。
