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  1. Article ; Online: Numerical analysis of COVID-19 model with constant fractional order and variable fractal dimension.

    Alkahtani, Badr Saad T / Jain, Sonal

    Results in physics

    2020  Volume 20, Page(s) 103673

    Abstract: This work has considered a mathematical model describing the spread of COVID-19 in a given population. The model comprised 5 systems of equations that take into account different classes describing the impact of COVID-19 in a given population. The time ... ...

    Abstract This work has considered a mathematical model describing the spread of COVID-19 in a given population. The model comprised 5 systems of equations that take into account different classes describing the impact of COVID-19 in a given population. The time differential operator was replaced with three different types of nonlocal operators. These operators are defined as the convolution of variable order fractal differential operators with different kernels including power law, exponential decay law, and Mittag-Leffler functions. We presented the well-poseness of the models for different differential operators that were presented in detail. A novel numerical scheme was used to solve numerically the system and numerical simulations were provided.
    Language English
    Publishing date 2020-12-10
    Publishing country Netherlands
    Document type Journal Article
    ZDB-ID 2631798-9
    ISSN 2211-3797 ; 2211-3797
    ISSN (online) 2211-3797
    ISSN 2211-3797
    DOI 10.1016/j.rinp.2020.103673
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Article ; Online: On study of fractional order epidemic model of COVID-19 under non-singular Mittag-Leffler kernel.

    Alzaid, Sara Salem / Alkahtani, Badr Saad T

    Results in physics

    2021  Volume 26, Page(s) 104402

    Abstract: This paper investigates the analysis of the fraction mathematical model of the novel coronavirus (COVID-19), which is indeed a source of threat all over the globe. This paper deals with the transmission mechanism by some affected parameters in the ... ...

    Abstract This paper investigates the analysis of the fraction mathematical model of the novel coronavirus (COVID-19), which is indeed a source of threat all over the globe. This paper deals with the transmission mechanism by some affected parameters in the problem. The said study is carried out by the consideration of a fractional-order epidemic model describing the dynamics of COVID-19 under a non-singular kernel type of derivative. The concerned model examine via non-singular fractional-order derivative known as Atangana-Baleanu derivative in Caputo sense (ABC). The problem analyzes for qualitative analysis and determines at least one solution by applying the approach of fixed point theory. The uniqueness of the solution is derived by the Banach contraction theorem. For iterative solution, the technique of iterative fractional-order Adams-Bashforth scheme is applied. Numerical simulation for the proposed scheme is performed at various fractional-order lying between 0, 1 and for integer-order 1. We also compare the compartmental quantities of the said model at two different effective contact rates of
    Language English
    Publishing date 2021-06-12
    Publishing country Netherlands
    Document type Journal Article
    ZDB-ID 2631798-9
    ISSN 2211-3797 ; 2211-3797
    ISSN (online) 2211-3797
    ISSN 2211-3797
    DOI 10.1016/j.rinp.2021.104402
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  3. Article: A novel mathematics model of covid-19 with fractional derivative. Stability and numerical analysis.

    Alkahtani, Badr Saad T / Alzaid, Sara Salem

    Chaos, solitons, and fractals

    2020  Volume 138, Page(s) 110006

    Abstract: a mathematical model depicting the spread of covid-19 epidemic and implementation of population covid-19 intervention in Italy. The model has 8 components leading to system of 8 ordinary differential equations. In this paper, we investigate the model ... ...

    Abstract a mathematical model depicting the spread of covid-19 epidemic and implementation of population covid-19 intervention in Italy. The model has 8 components leading to system of 8 ordinary differential equations. In this paper, we investigate the model using the concept of fractional differential operator. A numerical method based on the Lagrange polynomial was used to solve the system equations depicting the spread of COVID-19. A detailed investigation of stability including reproductive number using the next generation matrix, and the Lyapunov were presented in detail. Numerical simulations are depicted for various fractional orders.
    Keywords covid19
    Language English
    Publishing date 2020-06-17
    Publishing country England
    Document type Journal Article
    ZDB-ID 2003919-0
    ISSN 1873-2887 ; 0960-0779
    ISSN (online) 1873-2887
    ISSN 0960-0779
    DOI 10.1016/j.chaos.2020.110006
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  4. Article ; Online: A novel mathematics model of covid-19 with fractional derivative. Stability and numerical analysis

    Alkahtani, Badr Saad T. / Alzaid, Sara Salem

    Chaos, Solitons & Fractals

    2020  Volume 138, Page(s) 110006

    Keywords General Mathematics ; covid19
    Language English
    Publisher Elsevier BV
    Publishing country us
    Document type Article ; Online
    ZDB-ID 2003919-0
    ISSN 1873-2887 ; 0960-0779
    ISSN (online) 1873-2887
    ISSN 0960-0779
    DOI 10.1016/j.chaos.2020.110006
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  5. Article ; Online: New nonlinear model of population growth.

    T Alkahtani, Badr Saad / Atangana, Abdon / Koca, Ilknur

    PloS one

    2017  Volume 12, Issue 10, Page(s) e0184728

    Abstract: The model of population growth is revised in this paper. A new model is proposed based on the concept of fractional differentiation that uses the generalized Mittag-Leffler function as kernel of differentiation. The new model includes the choice of ... ...

    Abstract The model of population growth is revised in this paper. A new model is proposed based on the concept of fractional differentiation that uses the generalized Mittag-Leffler function as kernel of differentiation. The new model includes the choice of sexuality. The existence of unique solution is investigated and numerical solution is provided.
    MeSH term(s) Animals ; Female ; Humans ; Male ; Models, Theoretical ; Population Growth ; Sexuality
    Language English
    Publishing date 2017-10-24
    Publishing country United States
    Document type Journal Article
    ZDB-ID 2267670-3
    ISSN 1932-6203 ; 1932-6203
    ISSN (online) 1932-6203
    ISSN 1932-6203
    DOI 10.1371/journal.pone.0184728
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  6. Article: A novel mathematics model of covid-19 with fractional derivative. Stability and numerical analysis

    Alkahtani, Badr Saad T. / Alzaid, Sara Salem

    Chaos Solitons Fractals

    Abstract: a mathematical model depicting the spread of covid-19 epidemic and implementation of population covid-19 intervention in Italy. The model has 8 components leading to system of 8 ordinary differential equations. In this paper, we investigate the model ... ...

    Abstract a mathematical model depicting the spread of covid-19 epidemic and implementation of population covid-19 intervention in Italy. The model has 8 components leading to system of 8 ordinary differential equations. In this paper, we investigate the model using the concept of fractional differential operator. A numerical method based on the Lagrange polynomial was used to solve the system equations depicting the spread of COVID-19. A detailed investigation of stability including reproductive number using the next generation matrix, and the Lyapunov were presented in detail. Numerical simulations are depicted for various fractional orders.
    Keywords covid19
    Publisher WHO
    Document type Article
    Note WHO #Covidence: #605965
    Database COVID19

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  7. Article ; Online: New nonlinear model of population growth.

    Badr Saad T Alkahtani / Abdon Atangana / Ilknur Koca

    PLoS ONE, Vol 12, Iss 10, p e

    2017  Volume 0184728

    Abstract: The model of population growth is revised in this paper. A new model is proposed based on the concept of fractional differentiation that uses the generalized Mittag-Leffler function as kernel of differentiation. The new model includes the choice of ... ...

    Abstract The model of population growth is revised in this paper. A new model is proposed based on the concept of fractional differentiation that uses the generalized Mittag-Leffler function as kernel of differentiation. The new model includes the choice of sexuality. The existence of unique solution is investigated and numerical solution is provided.
    Keywords Medicine ; R ; Science ; Q
    Language English
    Publishing date 2017-01-01T00:00:00Z
    Publisher Public Library of Science (PLoS)
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  8. Article ; Online: Chaos on the Vallis Model for El Niño with Fractional Operators

    Badr Saad T. Alkahtani / Abdon Atangana

    Entropy, Vol 18, Iss 4, p

    2016  Volume 100

    Abstract: The Vallis model for El Niño is an important model describing a very interesting physical problem. The aim of this paper is to investigate and compare the models using both integer and non-integer order derivatives. We first studied the model with the ... ...

    Abstract The Vallis model for El Niño is an important model describing a very interesting physical problem. The aim of this paper is to investigate and compare the models using both integer and non-integer order derivatives. We first studied the model with the local derivative by presenting for the first time the exact solution for equilibrium points, and then we presented the exact solutions with the numerical simulations. We further examined the model within the scope of fractional order derivatives. The fractional derivatives used here are the Caputo derivative and Caputo–Fabrizio type. Within the scope of fractional derivatives, we presented the existence and unique solutions of the model. We derive special solutions of both models with Caputo and Caputo–Fabrizio derivatives. Some numerical simulations are presented to compare the models. We obtained more chaotic behavior from the model with Caputo–Fabrizio derivative than other one with local and Caputo derivative. When compare the three models, we realized that, the Caputo derivative plays a role of low band filter when the Caputo–Fabrizio presents more information that were not revealed in the model with local derivative.
    Keywords Vallis model ; chaotic behavior ; Caputo–Fabrizio fractional derivative ; analysis ; numerical simulations ; Science ; Q ; Astrophysics ; QB460-466 ; Physics ; QC1-999
    Subject code 518
    Language English
    Publishing date 2016-03-01T00:00:00Z
    Publisher MDPI AG
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  9. Article ; Online: Analysis of the Keller–Segel Model with a Fractional Derivative without Singular Kernel

    Abdon Atangana / Badr Saad T. Alkahtani

    Entropy, Vol 17, Iss 6, Pp 4439-

    2015  Volume 4453

    Abstract: Using some investigations based on information theory, the model proposed by Keller and Segel was extended to the concept of fractional derivative using the derivative with fractional order without singular kernel recently proposed by Caputo and Fabrizio. ...

    Abstract Using some investigations based on information theory, the model proposed by Keller and Segel was extended to the concept of fractional derivative using the derivative with fractional order without singular kernel recently proposed by Caputo and Fabrizio. We present in detail the existence of the coupled-solutions using the fixed-point theorem. A detailed analysis of the uniqueness of the coupled-solutions is also presented. Using an iterative approach, we derive special coupled-solutions of the modified system and we present some numerical simulations to see the effect of the fractional order.
    Keywords Keller–Segel model ; Caputo–Fabrizio fractional derivative ; fixed-point theorem ; special solution ; Science ; Q ; Astrophysics ; QB460-466 ; Physics ; QC1-999
    Language English
    Publishing date 2015-06-01T00:00:00Z
    Publisher MDPI AG
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  10. Article ; Online: Analytical Solution of Space-Time Fractional Fokker-Planck Equation by Homotopy Perturbation Sumudu Transform Method

    Ravi Shanker Dubey / Badr Saad T. Alkahtani / Abdon Atangana

    Mathematical Problems in Engineering, Vol

    2014  Volume 2014

    Keywords Mathematics ; QA1-939 ; Science ; Q ; Engineering (General). Civil engineering (General) ; TA1-2040 ; Technology ; T
    Language English
    Publishing date 2014-01-01T00:00:00Z
    Publisher Hindawi Publishing Corporation
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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