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

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Citation - WoS: 36
Citation - Scopus: 36
A hybrid fractional optimal control for a novel Coronavirus (2019-nCov) mathematical model
(Elsevier, 2021) Sweilam, N. H.; AL-Mekhlafi, S. M.; Baleanu, D.; 56389; Matematik
Introduction: Coronavirus COVID-19 pandemic is the defining global health crisis of our time and the greatest challenge we have faced since world war two. To describe this disease mathematically, we noted that COVID-19, due to uncertainties associated to the pandemic, ordinal derivatives and their associated integral operators show deficient. The fractional order differential equations models seem more consistent with this disease than the integer order models. This is due to the fact that fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes. Hence there is a growing need to study and use the fractional order differential equations. Also, optimal control theory is very important topic to control the variables in mathematical models of infectious disease. Moreover, a hybrid fractional operator which may be expressed as a linear combination of the Caputo fractional derivative and the Riemann-Liouville fractional integral is recently introduced. This new operator is more general than the operator of Caputo's fractional derivative. Numerical techniques are very important tool in this area of research because most fractional order problems do not have exact analytic solutions. Objectives: A novel fractional order Coronavirus (2019-nCov) mathematical model with modified parameters will be presented. Optimal control of the suggested model is the main objective of this work. Three control variables are presented in this model to minimize the number of infected populations. Necessary control conditions will be derived. Methods: The numerical methods used to study the fractional optimality system are the weighted average nonstandard finite difference method and the Grunwald-Letnikov nonstandard finite difference method. Results: The proposed model with a new fractional operator is presented. We have successfully applied a kind of Pontryagin's maximum principle and were able to reduce the number of infected people using the proposed numerical methods. The weighted average nonstandard finite difference method with the new operator derivative has the best results than Grunwald-Letnikov nonstandard finite difference method with the same operator. Moreover, the proposed methods with the new operator have the best results than the proposed methods with Caputo operator. Conclusions: The combination of fractional order derivative and optimal control in the Coronavirus (2019-nCov) mathematical model improves the dynamics of the model. The new operator is more general and suitable to study the optimal control of the proposed model than the Caputo operator and could be more useful for the researchers and scientists. (C) 2021 The Authors. Published by Elsevier B.V. on behalf of Cairo University.
Citation - WoS: 29
Citation - Scopus: 36
Comparative study for optimal control nonlinear variable -order fractional tumor model
(Pergamon-elsevier Science Ltd, 2020) Sweilam, N. H.; AL-Mekhlafi, S. M.; Alshomrani, A. S.; Baleanu, D.; 56389; Matematik
Citation - WoS: 14
Citation - Scopus: 17
Efficient numerical treatments for a fractional optimal control nonlinear Tuberculosis model
(World Scientific Publ Co Pte Ltd, 2018) Sweilam, N. H.; AL-Mekhlafi, S. M.; Baleanu, D.; 56389; Matematik
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.
Citation - WoS: 15
Citation - Scopus: 19
Nonstandard finite difference method for solving complex-order fractional Burgers’ equations
(Elsevier, 2020) Sweilam, N. H.; AL-Mekhlafi, S. M.; Baleanu, D.; 56389; Matematik
The aim of this work is to present numerical treatments to a complex order fractional nonlinear one-dimensional problem of Burgers' equations. A new parameter sigma(t) is presented in order to be consistent with the physical model problem. This parameter characterizes the existence of fractional structures in the equations. A relation between the parameter sigma(t) and the time derivative complex order is derived. An unconditionally stable numerical scheme using a kind of weighted average nonstandard finite-difference discretization is presented. Stability analysis of this method is studied. Numerical simulations are given to confirm the reliability of the proposed method. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University.
Citation - WoS: 84
Citation - Scopus: 101
Optimal control for a fractional tuberculosis infection model including the impact of diabetes and resistant strains
(Elsevier Science Bv, 2019) Sweilam, N. H.; AL-Mekhlafi, S. M.; Baleanu, D.; 56389; Matematik
The objective of this paper is to study the optimal control problem for the fractional tuberculosis (TB) infection model including the impact of diabetes and resistant strains. The governed model consists of 14 fractional-order (FO) equations. Four control variables are presented to minimize the cost of interventions. The fractional derivative is defined in the Atangana-Baleanu-Caputo (ABC) sense. New numerical schemes for simulating a FO optimal system with Mittag-Leffler kernels are presented. These schemes are based on the fundamental theorem of fractional calculus and Lagrange polynomial interpolation. We introduce a simple modification of the step size in the two-step Lagrange polynomial interpolation to obtain stability in a larger region. Moreover, necessary and sufficient conditions for the control problem are considered. Some numerical simulations are given to validate the theoretical results. (C) 2019 The Authors. Published by Elsevier B.V. on behalf of Cairo University.
Citation - WoS: 34
Citation - Scopus: 42
Optimal control for variable order fractional HIV/AIDS and malaria mathematical models with multi-time delay
(Elsevier, 2020) Sweilam, N. H.; AL-Mekhlafi, S. M.; Mohammed, Z. N.; Baleanu, D.; 56389; Matematik
In this article, optimal control for variable order fractional multi-delay mathematical model for the co-infection of HIV/AIDS and malaria is presented. This model consists of twelve differential equations, where the variable order derivative are in the sense of Caputo. Three control variables are presented in this model to minimize the number of the co-infected individuals showing no symptoms of AIDS, the infected individuals with malaria, and the individuals asymptomatically infected with HIV/AIDS. Necessary conditions for the control problem are derived. The Grunwald-Letnikov nonstandard finite difference scheme is constructed to simulating the proposed optimal control system. The stability of the proposed scheme is proved. In order to validate the theoretical results numerical simulations and comparative studies are given. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.