Aminikhah Hossein, Malekzadeh Nasrin
Department of Applied Mathematics, School of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht 41938, Iran.
ScientificWorldJournal. 2013 Oct 10;2013:687695. doi: 10.1155/2013/687695. eCollection 2013.
A new homotopy perturbation method (NHPM) is applied to system of variable coefficient coupled Burgers' equation with time-fractional derivative. The fractional derivatives are described in the Caputo fractional derivative sense. The concept of new algorithm is introduced briefly, and NHPM is examined for two systems of nonlinear Burgers' equation. In this approach, the solution is considered as a power series expansion that converges rapidly to the nonlinear problem. The new approximate analytical procedure depends on two iteratives. The modified algorithm provides approximate solutions in the form of convergent series with easily computable components. Results indicate that the introduced method is promising for solving other types of systems of nonlinear fractional-order partial differential equations.
一种新的同伦摄动方法（NHPM）被应用于具有时间分数阶导数的变系数耦合伯格斯方程系统。分数阶导数是在卡普托分数阶导数意义下描述的。简要介绍了新算法的概念，并针对两个非线性伯格斯方程系统检验了NHPM。在这种方法中，解被视为一个快速收敛到非线性问题的幂级数展开。新的近似解析过程依赖于两个迭代。改进后的算法以具有易于计算的分量的收敛级数形式提供近似解。结果表明，所提出的方法在求解其他类型的非线性分数阶偏微分方程系统方面具有前景。
