基于Mittag-Leffler幂律的冠状病毒-19疾病建模

IF 4.1 3区数学 Q1 Mathematics Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-09-11 DOI:10.1186/s13662-020-02943-z

Samia Bushnaq, Kamal Shah, Hussam Alrabaiah

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引用次数: 8

摘要

本文研究了Mittag-Leffler型衍生的新型冠状病毒病(COVID-19)易感类、感染类和恢复类3个区室模型。上述衍生词由Atangana、Baleanu和Caputo引入，缩写为(ABC)。利用不动点理论，首先证明了所考虑的模型至少有一个解的存在性和唯一性。同时也得到了一些关于Ulam-Hyers型稳定性的结果。通过应用一种称为分数Adams-Bashforth (AB)方法的数值技术，我们开发了一个所考虑模型的近似解方案。利用一些实际可用数据，对不同分数阶值进行了相应的数值模拟。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On modeling of coronavirus-19 disease under Mittag-Leffler power law.

This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivative has been introduced by Atangana, Baleanu, and Caputo abbreviated as $(ABC)$ . Upon utilizing fixed point theory, we first prove the existence of at least one solution for the considered model and its uniqueness. Also, some results about stability of Ulam-Hyers type are also established. By applying a numerical technique called fractional Adams-Bashforth (AB) method, we develop a scheme for the approximate solutions to the considered model. Using some real available data, we perform the concerned numerical simulation corresponding to different values of fractional order.

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来源期刊

Advances in Difference Equations 数学-数学

自引率

0.00%

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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.