On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation
On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation
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DOI：
10.1016/j.amc.2015.10.021
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发表时间：
2016-01-15
影响因子：
4
通讯作者：
Atangana, Abdon
中科院分区：
文献类型：
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作者：
Atangana, Abdon
最近Caputo和Fabrizio介绍了一种新的分数阶导数。在本文中，我们提供了有用的工具，新的导数，并将其应用到非线性Fisher的反应扩散方程。利用迭代法的概念给出了修正方程的解。利用不动点理论，证明了所用方法的稳定性。给出了不同分数阶数下的数值模拟结果。(C)2015 Elsevier Inc. All rights reserved.
Recently Caputo and Fabrizio introduced a new derivative with fractional order. In this paper, we presented useful tools about the new derivative and applied it to the nonlinear Fisher's reaction-diffusion equation. We presented the solution of the modified equation using the notion of iterative method. Using the theory of fixed point, we presented the stability of the used method. Some numerical simulations were presented for different values of fractional order. (C) 2015 Elsevier Inc. All rights reserved.