On the dynamics of fractional maps with power-law, exponential decay and Mittag–Leffler memory

Ávalos-Ruiz, L.F.; Gómez‐Aguilar, J.F.; Atangana, Abdon; Owolabi, Kolade M.

doi:10.1016/j.chaos.2019.07.010

Cited by 45 publications

(15 citation statements)

References 28 publications

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“…For the purpose of above, Now applying the Caputo-Fabrizio fractional derivative [13] , [34] , [35] , [36] , [37] , [38] , [39] in the classical mathematical model (3.1) . The fractional order transmission model for COVID-19 dynamics is given by the following system of non-linear fractional differential equation;…”

Section: Formulation Of the Mathematical Modelmentioning

confidence: 99%

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A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China

Yadav

Verma

2020

Chaos, Solitons & Fractals

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The novel Covid-19 was identified in Wuhan China in December, 2019 and has created medical emergency world wise and distorted many life in the couple of month, it is being burned challenging situation for the medical scientist and virologists. Fractional order derivative based modeling is quite important to understand the real world problems and to analyse realistic situation of the proposed model. In the present investigation a fractional model based on Caputo-Fabrizio fractional derivative has been developed for the transmission of CORONA VIRUS (COVID-19) in Wuhan China. The existence and uniqueness solutions of the fractional order derivative has been investigated with the help of fixed point theory. Adamas- Bashforth numerical scheme has been used in the numerical simulation of the Caputo-Fabrizio fractional order derivative. The analysis of susceptible population, exposed population, infected population, recovered population and concentration of the virus of COVID-19 in the surrounding environment with respect to time for different values of fractional order derivative has been shown by means of graph. The comparative analysis has also been performed from classical model and fractional model along with the certified experimental data.

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Section: Formulation Of the Mathematical Modelmentioning

confidence: 99%

“…The Caputo-Fabrizio (C-F) operator has attracted many research scholars due to the fact that it has a non-singular kernel and to be found most appropriate for modeling some class of real world problem. Some researcher [34] , [35] , [36] , [37] , [38] , [39] have been used in the modeling and have received tremendous success.…”

Section: Introductionmentioning

confidence: 99%

A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China

Yadav

Verma

2020

Chaos, Solitons & Fractals

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“…Later, the fractionalised model was developed further by adding an economic interest equation to the model [21] . More recently, in addition to using the Caputo derivative to study the complex behaviour of the phenomena, scholars applied the newly formulated fractional version of the Adams-Bashforth method in their research [22] , [23] , [24] , [25] , [26] , [27] . As another, for example, Kolade proposed a three-component time-fractional system representing the interaction among prey, intermediate-predators, and predators and examined the model behaviour under Caputo or the Atangana– Baleanu fractional derivatives [28] .…”

Section: Introductionmentioning

confidence: 99%

Memory and mutualism in species sustainability: A time-fractional Lotka-Volterra model with harvesting

Amirian

Towers

Jovanoski

et al. 2020

Heliyon

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We first present a predator-prey model for two species and then extend the model to three species where the two predator species engage in mutualistic predation. Constant effort harvesting and the impact of by-catch issue are also incorporated. Necessary sufficient conditions for the existence and stability of positive equilibrium points are examined. It is shown that harvesting is sustainable, and the memory concept of the fractional derivative damps out oscillations in the population numbers so that the system as a whole settles on an equilibrium quicker than it would with integer time derivatives. Finally, some possible physical explanations are given for the obtained results. It is shown that the stability requires the memory concept in the model.

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“…The aim of utilizing the AB fractional derivative to the model is that it has kernel is nonsingular and nonlocal, and the intersection behavior can be better described in the model using this operator than other fractional operators such as Caputo, Caputo-Fabrizio [23] , [24] , [25] , [26] , [27] , [28] , [29] , and other. Some recent research related to the AB fractional derivatives and their applications to different models emerging in science and engineering can be found in [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] . Some other related works to the modeling infectious diseases of AB fractional derivative can be seen in [39] , [40] , [41] , [42] , [43] , [44] , [45] .…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling for the outbreak of the coronavirus (COVID-19) under fractional nonlocal operator

Redhwan¹,

Abdo²,

Shah³

et al. 2020

Results in Physics

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A mathematical model for the spread of the COVID-19 disease based on a fractional Atangana–Baleanu operator is studied. Some fixed point theorems and generalized Gronwall inequality through the AB fractional integral are applied to obtain the existence and stability results. The fractional Adams–Bashforth is used to discuss the corresponding numerical results. A numerical simulation is presented to show the behavior of the approximate solution in terms of graphs of the spread of COVID-19 in the Chinese city of Wuhan. We simulate our table for the data of Wuhan from February 15, 2020 to April 25, 2020 for 70 days. Finally, we present a debate about the followed simulation in characterizing how the transmission dynamics of infection can take place in society.

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On the dynamics of fractional maps with power-law, exponential decay and Mittag–Leffler memory

Cited by 45 publications

References 28 publications

A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China

A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China

Memory and mutualism in species sustainability: A time-fractional Lotka-Volterra model with harvesting

Mathematical modeling for the outbreak of the coronavirus (COVID-19) under fractional nonlocal operator

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