Modified Auxiliary Equation Method versus Three Nonlinear Fractional Biological Models in Present Explicit Wave Solutions
Modified Auxiliary Equation Method versus Three Nonlinear Fractional Biological Models in Present Explicit Wave Solutions
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DOI：
10.3390/mca24010001
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发表时间：
2019-03-01
影响因子：
--
通讯作者：
Lu, Dianchen
中科院分区：
文献类型：
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作者：
Khater, Mostafa M. A.;Attia, Raghda A. M.;Lu, Dianchen
在本文中，我们提出了一种改进的辅助方程方法。我们在生物学科学分支的三个基本模型中利用这种修改。这些模型是生物种群模型、等宽模型和修正等宽方程。这三个模型分别代表了由于人口供给、沿正 x 方向传播的长波以及具有色散过程的非线性介质中一维波传播的模拟而产生的人口密度。我们在非线性分数阶偏微分方程公式中讨论这些模型。我们利用一致导数性质将它们转化为整数阶非线性常微分方程。适应后，我们对这些模型应用了新的修改，以获得它们的孤立解。我们获得了这些模型的许多新颖的解决方案，这有助于更多地了解它们的属性。所有获得的解都通过 Maple、Mathematica 和 Matlab 等计算机软件将它们带回到原始方程中进行验证。
In this article, we present a modified auxiliary equation method. We harness this modification in three fundamental models in the biological branch of science. These models are the biological population model, equal width model and modified equal width equation. The three models represent the population density occurring as a result of population supply, a lengthy wave propagating in the positive x-direction, and the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes, respectively. We discuss these models in nonlinear fractional partial differential equation formulas. We used the conformable derivative properties to convert them into nonlinear ordinary differential equations with integer order. After adapting, we applied our new modification to these models to obtain solitary solutions of them. We obtained many novel solutions of these models, which serve to understand more about their properties. All obtained solutions were verified by putting them back into the original equations via computer software such as Maple, Mathematica, and Matlab.