Novel analysis of the fractional Zika model using the Adams type predictor-corrector rule for non-singular and non-local fractional operators

Alkahtani, Badr Saad T.; Atangana, Abdon; Koca, İrfan

doi:10.22436/jnsa.010.06.32

Cited by 47 publications

(18 citation statements)

References 11 publications

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“…In [2], the authors used the concept of the generalized Mittag-Leffler function and the kernel was used as non-singular and non-local. The newly introduced A-B derivative has been applied to many real world complex problems successfully, which can be seen in [6,7,8,3]. The model of Ebola virus with A-B derivative is presented in [15].…”

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confidence: 99%

A fractional model for the dynamics of tuberculosis (TB) using Atangana-Baleanu derivative

Ullah¹,

Khan²,

Farooq³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - S

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In the present paper, we explore the dynamics of fractional tuberculosis model with Atangana-Baleanu (A-B) derivative. The number of confirmed notified cases reported by national tuberculosis control program (NTP) Khyber Pakhtunkhwa, Pakistan, since 2002 to 2017 are used for our analysis and estimation of the model parameters. Initially, the essential properties of the model are presented. We prove the existence of the solution through fixedpoint theory. Then, we show the uniqueness of the solution. Modified Adams-Bashforth technique is used to obtain the numerical solution of the fractional model. We obtain numerical results with different values of the fractional order parameters to show the importance of the newly proposed derivative, which provides useful information about the TB dynamics and its control.

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confidence: 99%

A fractional model for the dynamics of tuberculosis (TB) using Atangana-Baleanu derivative

Ullah¹,

Khan²,

Farooq³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - S

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“…Also, some studies in the biological models with fractional-order derivative have been conducted in recent years [36][37][38][39]. During last years researchers have been using some mathematical models to simulate the transmission of Zika virus [40][41][42][43].…”

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confidence: 99%

A new mathematical model for Zika virus transmission

2020

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We present a new mathematical model for the transmission of Zika virus between humans as well as between humans and mosquitoes. In this way, we use the fractional-order Caputo derivative. The region of the feasibility of system and equilibrium points are calculated, and the stability of equilibrium point is investigated. We prove the existence of a unique solution for the model by using the fixed point theory. By using the fractional Euler method, we get an approximate solution to the model. Numerical results are presented to investigate the effect of fractional derivative on the behavior of functions and also to compare the integer-order derivative and fractional-order derivative results.

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“…Chua's circuit model was analyzed with Atangana-Baleanu fractional derivative by Alkahtani [1]. A new analysis of the zika model was made for non-singular and non-local fractional operators [3]. Baskonus and Bulut also contributed to some articles on fractional derivatives [11][12][13][14]23].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Keller-Segel model with Atangana-Baleanu fractional derivative

Dokuyucu¹,

Băleanu²,

Çelık³

2018

Filomat

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The new definition of the fractional derivative was defined by Atangana and Baleanu in 2016. They used the generalized Mittag-Leffler function with the non-singular and non-local kernel. Further, their version provides all properties of fractional derivatives. Our aim is to analyse the Keller-Segel model with Caputo and Atangana-Baleanu fractional derivative in Caputo sense. Using fixed point theory, we first show the existence of coupled solutions. We then examine the uniqueness of these solutions. Finally, we compare our results numerically by modifying our model according to both definitions, and we demonstrate these results on the graphs in detail. All computations were done using Mathematica.

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Novel analysis of the fractional Zika model using the Adams type predictor-corrector rule for non-singular and non-local fractional operators

Cited by 47 publications

References 11 publications

A fractional model for the dynamics of tuberculosis (TB) using Atangana-Baleanu derivative

A fractional model for the dynamics of tuberculosis (TB) using Atangana-Baleanu derivative

A new mathematical model for Zika virus transmission

Analysis of Keller-Segel model with Atangana-Baleanu fractional derivative

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