Solving the fractional BBM–Burgers equation using the homotopy analysis method
Solving the fractional BBM–Burgers equation using the homotopy analysis method
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DOI：
10.1016/j.chaos.2007.09.042
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发表时间：
2009-05
影响因子：
7.8
通讯作者：
Lina Song;Hong-qing Zhang
中科院分区：
文献类型：
--
作者：
Lina Song;Hong-qing Zhang
利用同伦分析方法，通过用分数阶导数代替整数阶空间导数，得到了一类分数阶BBM-Burgers方程的近似解.分数阶导数在Caputo意义下描述。将传统的整数阶微分方程的同伦分析方法直接推广到分数阶微分方程的显式求解和数值求解。我们的模型方程的解计算的收敛级数的形式，易于计算的组件。
Based on the homotopy analysis method, a scheme is developed to obtain approximation solution of a fractional BBM–Burgers equation with initial condition, which is introduced by replacing some integer-order space derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the traditional homotopy analysis method for differential equations of integer-order is directly extended to derive explicit and numerical solutions of the fractional differential equations. The solutions of our model equation are calculated in the form of convergent series with easily computable components.