Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel

Morales‐Delgado, V. F.; Gómez‐Aguilar, J.F.; Taneco-Hernández, M.A.; Escobar-Jiménez, R.F.; Olivares-Peregrino, Víctor Hugo

doi:10.22436/jnsa.011.08.06

Cited by 25 publications

(14 citation statements)

References 19 publications

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“…The combination of Laplace transform and homotopy analysis technique makes an analytical method which is known as Modified Homotop Analysis Transform Method (MHATM) in the literature 39,41,42 . The main steps of the modified technique are written as follows: Step 1 .…”

Section: Fractional‐order Epidemic Model With Laplace Homotopy Methodsmentioning

confidence: 99%

“…The Liouville–Caputo fractional derivative (C) is presented as

_{t_{o}}^{c} D_{t}^{ξ} false{g false(t false) false} = \frac{1}{normalΓ false(1 - ξ false)} \int_{t_{o}}^{t} \frac{d}{d t} g false(τ false) {false(t - τ false)}^{- ξ}, n - 1 < ξ \leq n,

where gamma function is represented by Γ(.) 11,12,39,40 . Laplace transform for CF‐order derivative is as follows

scriptL false{_{t_{0}}^{C} D_{t}^{ξ} false{g false(t false) false} false} false(s false) = S^{ξ} G false(s false) - true \sum_{m - 1}^{k = 0} S^{ξ - k - 1} g^{false(k false)} false(0 false)

…”

Section: Preliminariesmentioning

confidence: 99%

“…Recently, a fractional derivative proposed by Atangana and Baleanu with the combination of Mittag‐Leffler function as the kernel of differentiation. This kernel is non‐singular and nonlocal in character and has benefits of the above mentioned Liouville–Caputo derivative as preservation 39,40 …”

Section: Preliminariesmentioning

confidence: 99%

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Modeling of fractional‐order COVID‐19 epidemic model with quarantine and social distancing

Farman

Aslam

Akgül

et al. 2021

Math Methods in App Sciences

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Different countries of the world are facing a serious pandemic of corona virus disease (COVID‐19). One of the most typical treatments for COVID‐19 is social distancing, which includes lockdown; it will help to decrease the number of contacts for undiagnosed individuals. The main aim of this article is to construct and evaluate a fractional‐order COVID‐19 epidemic model with quarantine and social distancing. Laplace homotopy analysis method is used for a system of fractional differential equation (FDEs) with Caputo and Atangana–Baleanu–Caputo (ABC) fractional derivative. By applying the ABC and Caputo derivative, the numerical solution for fractional‐order COVID‐19 epidemic model is achieved. The uniqueness and existence of the solution is checked by Picard–Lindelof's method. The proposed fractional model is demonstrated by numerical simulation which is useful for the government to control the spread of disease in a practical way.

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Section: Fractional‐order Epidemic Model With Laplace Homotopy Methodsmentioning

confidence: 99%

“…The Liouville–Caputo fractional derivative (C) is presented as

_{t_{o}}^{c} D_{t}^{ξ} false{g false(t false) false} = \frac{1}{normalΓ false(1 - ξ false)} \int_{t_{o}}^{t} \frac{d}{d t} g false(τ false) {false(t - τ false)}^{- ξ}, n - 1 < ξ \leq n,

where gamma function is represented by Γ(.) 11,12,39,40 . Laplace transform for CF‐order derivative is as follows

scriptL false{_{t_{0}}^{C} D_{t}^{ξ} false{g false(t false) false} false} false(s false) = S^{ξ} G false(s false) - true \sum_{m - 1}^{k = 0} S^{ξ - k - 1} g^{false(k false)} false(0 false)

…”

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

Modeling of fractional‐order COVID‐19 epidemic model with quarantine and social distancing

Farman

Aslam

Akgül

et al. 2021

Math Methods in App Sciences

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show abstract

“…Recently, the AB derivative has been used in modeling various real world phenomena, for example see [42] , [43] . Further, AB derivative has also used to model various infectious diseases like Ebola virus, dynamics of smoking, Leptospirosis, etc [44] , [45] , [46] , [47] , [48] , [49] , [50] , [51] in more comprehensive way.…”

Section: Introductionmentioning

confidence: 99%

Computational and theoretical modeling of the transmission dynamics of novel COVID-19 under Mittag-Leffler Power Law

Sher

Shah

Khan

et al. 2020

Alexandria Engineering Journal

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In the current article, we studied the novel corona virus (2019-nCoV or COVID-19) which is a threat to the whole world nowadays. We consider a fractional order epidemic model which describes the dynamics of COVID-19 under nonsingular kernel type of fractional derivative. An attempt is made to discuss the existence of the model using the fixed point theorem of Banach and Krasnoselskii’s type. We will also discuss the Ulam-Hyers type of stability of the mentioned problem. For semi analytical solution of the problem the Laplace Adomian decomposition method (LADM) is suggested to obtain the required solution. The results are simulated via Matlab by graphs. Also we have compare the simulated results with some reported real data for Commutative class at classical order.

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“…Furthermore, there are many studies in the literature, which are modeled by the fractional concept related to diseases and bad habits [21][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

System Analysis of HIV Infection Model with CD4⁺ T under Non-Singular Kernel Derivative

Evirgen

Uçar

Özdemir

2020

Applied Mathematics and Nonlinear Sciences

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Infectious diseases have caused the death of many people throughout the world for centuries. For this purpose, many researchers have investigated these diseases for establishing new treatment and protective measures. The most important of these is HIV disease. In this study, an HIV infection model of CD4+T cells is handled comprehensively with the newly defined Atangana-Baleanu (AB) fractional derivative. The existence and uniqueness of the solutions for fractionalized HIV disease model with the new derivative by considering the Arzela-Ascoli theorem.

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Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel

Cited by 25 publications

References 19 publications

Modeling of fractional‐order COVID‐19 epidemic model with quarantine and social distancing

Modeling of fractional‐order COVID‐19 epidemic model with quarantine and social distancing

Computational and theoretical modeling of the transmission dynamics of novel COVID-19 under Mittag-Leffler Power Law

System Analysis of HIV Infection Model with CD4⁺ T under Non-Singular Kernel Derivative

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Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel

Cited by 25 publications

References 19 publications

Modeling of fractional‐order COVID‐19 epidemic model with quarantine and social distancing

Modeling of fractional‐order COVID‐19 epidemic model with quarantine and social distancing

Computational and theoretical modeling of the transmission dynamics of novel COVID-19 under Mittag-Leffler Power Law

System Analysis of HIV Infection Model with CD4+ T under Non-Singular Kernel Derivative

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System Analysis of HIV Infection Model with CD4⁺ T under Non-Singular Kernel Derivative