Browsing by Author "Alzahrani, Ebraheem"

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Citation Count: Bhrawy, A.H...et al. (2016). A chebyshev-laguerre-gauss-radau collocation scheme for solving a time fractional sub-diffusion equation on a semi-infinite domain. Proceedings Of The Romanian Academy Series A-Mathematics Physics Technical Science Information Science, 16(4), 490-498.
A chebyshev-laguerre-gauss-radau collocation scheme for solving a time fractional sub-diffusion equation on a semi-infinite domain
(The Publishing House of the Romanian Academy, 2015) Bhrawy, A. H.; Abdelkawy, M. A.; Alzahrani, A. A.; Baleanu, Dumitru; Alzahrani, Ebraheem
We propose a new efficient spectral collocation method for solving a time fractional sub-diffusion equation on a semi-infinite domain. The shifted Chebyshev-Gauss-Radau interpolation method is adapted for time discretization along with the Laguerre-Gauss-Radau collocation scheme that is used for space discretization on a semi-infinite domain. The main advantage of the proposed approach is that a spectral method is implemented for both time and space discretizations, which allows us to present a new efficient algorithm for solving time fractional sub-diffusion equations
Citation Count: Bhrawy, A.H...et al. (2015). Generalized Laguerre-Gauss-Radau scheme for first order hyperbolic equations on semi-infinite domains. Romanian Journal of Physics, 60(7-8), 918-934.
Generalized Laguerre-Gauss-Radau scheme for first order hyperbolic equations on semi-infinite domains
(Editura Academiei Romane, 2015) Bhrawy, A. H.; Hafez, R. M.; Alzahrani, Ebraheem; Baleanu, Dumitru; Alzahrani, A. A.
In this article, we develop a numerical approximation for first-order hyperbolic equations on semi-infinite domains by using a spectral collocation scheme. First, we propose the generalized Laguerre-Gauss-Radau collocation scheme for both spatial and temporal discretizations. This in turn reduces the problem to the obtaining of a system of algebraic equations. Second, we use a Newton iteration technique to solve it. Finally, the obtained results are compared with the exact solutions, highlighting the performance of the proposed numerical method.
Citation Count: Alzahrani, Ebraheem; El-Dessoky, M.M.; Baleanu, Dumitru (2021). "Mathematical modeling and analysis of the novel Coronavirus using Atangana–Baleanu derivative", Results in Physics, Vol. 25.
Mathematical modeling and analysis of the novel Coronavirus using Atangana–Baleanu derivative
(2021) Alzahrani, Ebraheem; El-Dessoky, M.M.; Baleanu, Dumitru; 56389
The novel Coronavirus infection disease is becoming more complex for the humans society by giving death and infected cases throughout the world. Due to this infection, many countries of the world suffers from great economic loss. The researchers around the world are very active to make a plan and policy for its early eradication. The government officials have taken full action for the eradication of this virus using different possible control strategies. It is the first priority of the researchers to develop safe vaccine against this deadly disease to minimize the infection. Different approaches have been made in this regards for its elimination. In this study, we formulate a mathematical epidemic model to analyze the dynamical behavior and transmission patterns of this new pandemic. We consider the environmental viral concentration in the model to better study the disease incidence in a community. Initially, the model is constructed with the derivative of integer-order. The classical epidemic model is then reconstructed with the fractional order operator in the form of Atangana–Baleanu derivative with the nonsingular and nonlocal kernel in order to analyze the dynamics of Coronavirus infection in a better way. A well-known estimation approach is used to estimate model parameters from the COVID-19 cases reported in Saudi Arabia from March 1 till August 20, 2020. After the procedure of parameters estimation, we explore some basic mathematical analysis of the fractional model. The stability results are provided for the disease free case using fractional stability concepts. Further, the uniqueness and existence results will be shown using the Picard–Lendelof approach. Moreover, an efficient numerical scheme has been proposed to obtain the solution of the model numerically. Finally, using the real fitted parameters, we depict many simulation results in order to demonstrate the importance of various model parameters and the memory index on disease dynamics and possible eradication. © 2021 The Authors
Citation Count: Alzahrani, Ebraheem; El-Dessoky, M.M.; Baleanu, Dumitru (2021).Modeling the dynamics of the novel coronavirus using Caputo-Fabrizio derivative " Alexandria Engineering Journal, Vol. 60, No. 5, pp. 4651-4662.
Modeling the dynamics of the novel coronavirus using Caputo-Fabrizio derivative
(2021) Alzahrani, Ebraheem; El-Dessoky, M.M.; Baleanu, Dumitru; 56389
The virus that begins from Wuhan China, known as COVID-19 or coronavirus is still a huge panic for humans around the globe. The elimination of this virus from our society needs proper attentions to follows the rule suggested by World Health Organization (WHO). A vast literature on the modeling of this infection in various perspective is available. In the present work, we design a new mathematical model for COVID-19 pandemic by utilizing the real infected cases reported from Kingdom of Saudi Arabia. Initially, we formulate the model with the help of classical integer order nonlinear differential equations. The treatment class is considered the model to analyze the impact of treatment on the disease dynamics. The Caputo-Fabrizio derivative with the non-singular exponential kernel is applied in order to reformulate the proposed COVID-19 transmission model with a fractional order. The biologically important parameter called the basic reproductive number is investigated both theoretically and numerically. The estimated values of R0 for the selected period are approximated to be 1.63. Further, by making use of the Picard Lindelöf theorem we provide the existence and uniqueness of the COVID-19 fractional epidemic model. Moreover, the fractional model is solved numerically and a number of simulation results are depicted using the real estimated parameters. The impact of various model parameters and memory index are shown graphically. We conclude that the fractional order epidemic models are more appropriate and provide deep insights into the disease dynamics. © 2021 THE AUTHORS
Citation Count: Bhrawy, Ali H...et.al. (2015). "New operational matrices for solving fractional differential equations on the half-line", Plos One, Vol.10, No.9, pp.1-23.
New operational matrices for solving fractional differential equations on the half-line
(Public Library Science, 2015) Bhrawy, Ali H.; Taha, Taha M.; Alzahrani, Ebraheem; Baleanu, Dumitru; Alzahrani, Abdulrahim A.; 56389
In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.