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On the stability analysis for a semi-analytical scheme for solving the fractional order blood ethanol concentration system using LVIM

Adel Mohamed, Sweilam Nasser H., Khader Mohamed M.

Journal of Applied Mathematics and Computational Mechanics

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2024

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Vol. 23, nr 1

7-18

EN

The purpose of this article is to present the Laplace variational iteration method, which combines the VIM with the Laplace transform approach (LVIM). This combination will result in a better and more quickly convergent sequence since nonlinear fractional differential equations (FDEs) cannot be solved using the Laplace transform. With the use of the fixed point theory, the stability analysis is specifically discussed and examined. The blood ethanol concentration system is solved numerically by using the suggested scheme. This model can be represented by a system of FDEs. The investigation will emploi the Caputo-Fabrizio fractional derivative. To provide a more in-depth study of this model, we have taken it in its fractional form so that we can more accurately follow the behavior of the solution in the future and history based on the memory effect of fractional derivatives. We determine the accuracy and efficiency of the provided process by evaluating the absolute errors, and a comparison with the existing published work. The results show that the approach is a useful tool for simulating this model.

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Semi-analytical scheme with its stability analysis for solving the fractional-order predator-prey equations by using Laplace-VIM

Adel Mohamed, Sweilam Nasser H., Khader Mohamed M.

Journal of Applied Mathematics and Computational Mechanics

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2023

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Vol. 22, nr 4

5-17

EN

The article’s goal is to implement a semi-analytical technique named, the Laplace variational iteration method (LVIM), which is the combination of VIM and Laplace transform method. Although both the Laplace transform method and VIM cannot be applied to some nonlinear fractional differential equations (FDEs) individually, this combination will give a fast-convergent solution to the problem under study. The proposed scheme is used to numerically solve a biodynamic system called the Lotka-Volterra system, i.e. Predator-Prey Equations (PPEs). The system of FDEs can be used to represent this scenario, as well as the Caputo-Fabrizio fractional derivative will be used throughout the study. By assessing the residual error function, we can confirm that the given procedure is effective and accurate. The outcomes demonstrate that the technique used is an effective tool for simulating such models.

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Influence of ventilation to limit airborne infection concentration in an isolation room

Kassem Fatma A.-M., Abdelgawad Ahmed Farouk, Abu El-Ezz A. E., Nassief Mofreh M., Adel Mohamed

Environment Protection Engineering

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2023

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Vol. 49, nr 2

39--54

EN

Coronavirus (COVID-19) was detected at the end of 2019 and has since caused a worldwide pandemic. This virus is transferred airborne. In this study, an investigation was carried out of the ventilation strategies inside the isolation room based on exhaust air locations. To reduce the infection disease (COVID-19), due to the spreading of exhaled contaminants by humans in interior environments, five models for ventilation systems differing in the position of the outlet and inlet were used. This study aims to increase knowledge regarding the exhaled contaminant distribution under different environ-mental conditions (opening exhaust and negative pressure). The results showed a good agreement be-tween the computational results and the experimental data. Tracer gas CO2 was used to evaluate the air quality experimentally and computationally. The results showed that stable conditions are obtained inside the room at a negative pressure value above –1.5 Pa. The residence time of the infected airborne decreases when the pressure difference increases. The study revealed that the model with an air outlet opening installed behind the patient enabled avoiding the spread of infection in the room.