Analysis of some generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si12.svg"><mml:mrow><mml:mi mathvariant="italic">ABC</mml:mi></mml:mrow></mml:math> – Fractional logistic models

Abdeljawad, Thabet; Hajji, Mohamed; Al‐Mdallal, Qasem M.; Jarad, Fahd

doi:10.1016/j.aej.2020.01.030

Cited by 55 publications

(21 citation statements)

References 27 publications

(40 reference statements)

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“…Since for the nonlinear problems mostly it is difficult to find their exact solution. Therefore various numerical procedures (methods) have been constructed in literature to deal such like problem, see [31] , [32] , [33] , [34] , [35] , [36] , [41] , [46] . Therefore a famous Haar collocation method is applied to simulate the results via the use of Matlab-16.…”

Section: Introductionmentioning

confidence: 99%

Haar wavelet collocation approach for the solution of fractional order COVID-19 model using Caputo derivative

Shah

Khan

Ali³

et al. 2020

Alexandria Engineering Journal

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This article is devoted to study a compartmental mathematical model for the transmission dynamics of the novel Coronavirus-19 under Caputo fractional order derivative. By using fixed point theory of Schauder’s and Banach we establish some necessary conditions for existence of at least one solution to model under investigation and its uniqueness. After the existence a general numerical algorithm based on Haar collocation method is established to compute the approximate solution of the model. Using some real data we simulate the results for various fractional order using Matlab to reveal the transmission dynamics of the current disease due to Coronavirus-19 through graphs.

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Section: Introductionmentioning

confidence: 99%

Haar wavelet collocation approach for the solution of fractional order COVID-19 model using Caputo derivative

Shah

Khan

Ali³

et al. 2020

Alexandria Engineering Journal

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“…Thus, it is meaningful to study the proposed TB model in feasible region . For the upcoming results, we suggest the readers some recent related results for the stabilities and numerical techniques given in [23][24][25][26][27][28][29].…”

Section: Lemma 22mentioning

confidence: 99%

Stability analysis of a dynamical model of tuberculosis with incomplete treatment

et al. 2020

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A simple deterministic epidemic model for tuberculosis is addressed in this article. The impact of effective contact rate, treatment rate, and incomplete treatment versus efficient treatment is investigated. We also analyze the asymptotic behavior, spread, and possible eradication of the TB infection. It is observed that the disease transmission dynamics is characterized by the basic reproduction ratio $\Re _{0}$ ℜ 0 ; if $\Re _{0}<1$ ℜ 0 < 1 , there is only a disease-free equilibrium which is both locally and globally asymptotically stable. Moreover, for $\Re _{0}>1$ ℜ 0 > 1 , a unique positive endemic equilibrium exists which is globally asymptotically stable. The global stability of the equilibria is shown via Lyapunov function. It is also obtained that incomplete treatment of TB causes increase in disease infection while efficient treatment results in a reduction in TB. Finally, for the estimated parameters, some numerical simulations are performed to verify the analytical results. These numerical results indicate that decrease in the effective contact rate λ and increase in the treatment rate γ play a significant role in the TB infection control.

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“…Particularly, with the revolution in computer technology and symbolic programming, many new algorithms are proposed by many mathematicians, engineers and physicists. With the help of these techniques, many researchers analyze various classes of nonlinear systems and present some simulating results [12–56]. For instance, authors in [34, 35] studied logistic models within the frame of FC and illustrated some interesting consequences.…”

Section: Introductionmentioning

confidence: 99%

New numerical simulation for fractional Benney–Lin equation arising in falling film problems using two novel techniques

Gao

Veeresha

Prakasha

et al. 2020

Numerical Methods Partial

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The pivotal aim of the present work is to find the numerical solution for fractional Benney-Lin equation by using two efficient methods, called q-homotopy analysis transform method and fractional natural decomposition method. The considered equation exemplifies the long waves on the liquid films. Projected methods are distinct with solution procedure and they are modified with different transform algorithms. To illustrate the reliability and applicability of the considered solution procedures we consider eight special cases with different initial conditions. The fractional operator is considered in Caputo sense. The achieved results are drowned through two and three-dimensional plots for different Brownian motions and classical order. The numerical simulations are presented to ensure the efficiency of considered techniques. The behavior of the obtained results for distinct fractional order is captured in the present framework. The outcomes of the present investigation show that, the considered schemes are efficient and powerful to solve nonlinear differential equations arise in science and technology.

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Analysis of some generalized ABC – Fractional logistic models

Cited by 55 publications

References 27 publications

Haar wavelet collocation approach for the solution of fractional order COVID-19 model using Caputo derivative

Haar wavelet collocation approach for the solution of fractional order COVID-19 model using Caputo derivative

Stability analysis of a dynamical model of tuberculosis with incomplete treatment

New numerical simulation for fractional Benney–Lin equation arising in falling film problems using two novel techniques

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