Browsing by Author "Al-Mekhlafi, S. M."

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A hybrid stochastic fractional order Coronavirus (2019-nCov) mathematical model
(2021) Baleanu, Dumitru; Al-Mekhlafi, S. M.; Baleanu, Dumitru; 56389
In this paper, a new stochastic fractional Coronavirus (2019-nCov) model with modified parameters is presented. The proposed stochastic COVID-19 model describes well the real data of daily confirmed cases in Wuhan. Moreover, a novel fractional order operator is introduced, it is a linear combination of Caputo's fractional derivative and Riemann-Liouville integral. Milstein's higher order method is constructed with the new fractional order operator to study the model problem. The mean square stability of Milstein algorithm is proved. Numerical results and comparative studies are introduced.
Comparative study for optimal control nonlinear variable -order fractional tumor model
(2020) Baleanu, Dumitru; Al-Mekhlafi, S. M.; Alshomrani, A. S.; Baleanu, Dumitru; 56389
Comparative Study for Optimal Control Nonlinear Variable-Order Fractional Tumor Model
(Elsevier LTD., 2020) Baleanu, Dumitru; Al-Mekhlafi, S. M.; Alshomrani, Ali Saleh; Baleanu, Dumitru; 56389
Efficient numerical treatments for a fractional optimal control nonlinear Tuberculosis model
(World Scientific Publ CO PTE LTD, 2018) Baleanu, Dumitru; Al-Mekhlafi, S. M.; Baleanu, Dumitru; 56389
In this paper, the general nonlinear multi-strain Tuberculosis model is controlled using the merits of Jacobi spectral collocation method. In order to have a variety of accurate results to simulate the reality, a fractional order model of multi-strain Tuberculosis with its control is introduced, where the derivatives are adopted from Caputo's definition. The shifted Jacobi polynomials are used to approximate the optimality system. Subsequently, Newton's iterative method will be used to solve the resultant nonlinear algebraic equations. A comparative study of the values of the objective functional, between both the generalized Euler method and the proposed technique is presented. We can claim that the proposed technique reveals better results when compared to the generalized Euler method.
On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach
(2020) Baleanu, Dumitru; Al-Mekhlafi, S. M.; Albalawi, A. O.; Baleanu, Dumitru; 56389
In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grunwald-Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.