RETRACTED: New numerical method for ordinary differential equations: Newton polynomial

Atangana, Abdon; Araz, Seda İğret

doi:10.1016/j.cam.2019.112622

Cited by 65 publications

(40 citation statements)

References 11 publications

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“…In this section, we discuss the essential literature related to the fractal-fractional operator and its applications to the model of COVID-19. The flowing definitions are taken from [26].…”

Section: A Basic Of Fractal-fractional Calculus and Its Application Tmentioning

confidence: 99%

The dynamics of COVID-19 with quarantined and isolation

et al. 2020

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In the present paper, we formulate a new mathematical model for the dynamics of COVID-19 with quarantine and isolation. Initially, we provide a brief discussion on the model formulation and provide relevant mathematical results. Then, we consider the fractal-fractional derivative in Atangana-Baleanu sense, and we also generalize the model. The generalized model is used to obtain its stability results. We show that the model is locally asymptotically stable if R 0 < 1. Further, we consider the real cases reported in China since January 11 till April 9, 2020. The reported cases have been used for obtaining the real parameters and the basic reproduction number for the given period, R 0 ≈ 6.6361. The data of reported cases versus model for classical and fractal-factional order are presented. We show that the fractal-fractional order model provides the best fitting to the reported cases. The fractional mathematical model is solved by a novel numerical technique based on Newton approach, which is useful and reliable. A brief discussion on the graphical results using the novel numerical procedures are shown. Some key parameters that show significance in the disease elimination from the society are explored.

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“…In this section, we discuss the essential literature related to the fractal-fractional operator and its applications to the model of COVID-19. The flowing definitions are taken from [26].…”

Section: A Basic Of Fractal-fractional Calculus and Its Application Tmentioning

confidence: 99%

The dynamics of COVID-19 with quarantined and isolation

et al. 2020

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“…In this section, we construct a numerical scheme for fractional model based on the Caputo fractional derivative, CF fractional derivative and Atangana-Baleanu fractional derivative [6] . On applying this scheme we first consider the following non-linear fractional ODE:…”

Section: Numerical Solutionmentioning

confidence: 99%

Mathematical model of Ebola and Covid-19 with fractional differential operators: Non-Markovian process and class for virus pathogen in the environment

Zhang

Jain

2020

Chaos, Solitons & Fractals

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Differential operators based on convolution definitions have been recognized as powerful mathematics tools to help model real world problems due to the properties associated to their different kernels. In particular the power law kernel helps include into mathematical formulation the effect of long range, while the exponential decay helps with fading memory, also with Poisson distribution properties that lead to a transitive behavior from Gaussian to non-Gaussian phases respectively, however, with steady state in time and finally the generalized Mittag-Leffler helps with many features including the queen properties, transitive behaviors, random walk for earlier time and power law for later time. Very recently both Ebola and Covid-19 have been a great worry around the globe, thus scholars have focused their energies in modeling the behavior of such fatal diseases. In this paper, we used new trend of fractional differential and integral operators to model the spread of Ebola and Covid-19.

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“…They showed that the suggested numerical scheme is more accurate than the Adams-Bashforth method. 12 Example 1. We handle the following chaotic problem:…”

Section: Numerical Illustrationsmentioning

confidence: 99%

Atangana–seda Numerical Scheme for Labyrinth Attractor With New Differential and Integral Operators

Atangana

Araz

2020

Fractals

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In this paper, we present a new numerical scheme for a model involving new mathematical concepts that are of great importance for interpreting and examining real world problems. Firstly, we handle a Labyrinth chaotic problem with fractional operators which include exponential decay, power-law and Mittag-Leffler kernel. Moreover, this problem is solved via Atangana-Seda numerical scheme which is based on Newton polynomial. The accuracy and efficiency of the method can be easily seen with numerical simulations.

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RETRACTED: New numerical method for ordinary differential equations: Newton polynomial

Cited by 65 publications

References 11 publications

The dynamics of COVID-19 with quarantined and isolation

The dynamics of COVID-19 with quarantined and isolation

Mathematical model of Ebola and Covid-19 with fractional differential operators: Non-Markovian process and class for virus pathogen in the environment

Atangana–seda Numerical Scheme for Labyrinth Attractor With New Differential and Integral Operators

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