基于Caputo-Fabrizio导数的COVID-19传播分数阶微分方程模型

IF 4.1 3区数学 Q1 Mathematics Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-06-18 DOI:10.1186/s13662-020-02762-2

Dumitru Baleanu, Hakimeh Mohammadi, Shahram Rezapour

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引用次数: 144

摘要

我们提出了一个带有Caputo-Fabrizio导数的分数阶COVID-19传播模型。利用同伦分析方法与拉普拉斯变换相结合的同伦分析变换方法(HATM)对该问题进行了求解，并给出了收敛级数的近似解。利用不动点理论证明了迭代方法的唯一解的存在性和稳定性。我们还提出了模拟病毒传播的数值结果，并将结果与卡普托导数的结果进行了比较。

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A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative.

We present a fractional-order model for the COVID-19 transmission with Caputo-Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.

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来源期刊

Advances in Difference Equations 数学-数学

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.