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Browsing by Author "Al-Mekhlafi, Seham"

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    Citation - WoS: 21
    Citation - Scopus: 27
    Numerical Study for Two Types Variable-Order Burgers' Equations With Proportional Delay
    (Elsevier, 2020) Al-Mekhlafi, Seham; Shatta, Salma; Baleanu, Dumitru; Sweilam, Nasser
    In this paper, variable order Burgers' equations with proportional delays in time and space are studied. The variable order derivatives are defined in the sense of Atangana and Baleanu. Two types of variable order Atangana and Baleanu definitions are presented here. The nonstandard weighted average finite difference method is developed to study numerically the proposed models problem in one and two dimensional. Moreover, the stability analysis and truncation error are analyzed. Two test examples with proportional delays are given to characterizing the memory property of the proposed models. It is found that the proposed technique can be applied to study such variable-order fractional equations simply and effectively. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
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    Citation - WoS: 4
    Citation - Scopus: 6
    Numerical Treatments for the Optimal Control of Two Types Variable-Order Covid-19 Model
    (Elsevier, 2022) Al-Mekhlafi, Seham; Shatta, Salma; Baleanu, Dumitru; Sweilam, Nasser
    In this paper, a novel variable-order COVID-19 model with modified parameters is presented. The variable -order fractional derivatives are defined in the Caputo sense. Two types of variable order Caputo definitions are presented here. The basic reproduction number of the model is derived. Properties of the proposed model are studied analytically and numerically. The suggested optimal control model is studied using two numerical methods. These methods are non-standard generalized fourth-order Runge-Kutta method and the non-standard generalized fifth-order Runge-Kutta technique. Furthermore, the stability of the proposed methods are studied. To demonstrate the methodologies' simplicity and effectiveness, numerical test examples and comparisons with real data for Egypt and Italy are shown.