Yazar "Sultan, Muhammad" seçeneğine göre listele

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    Analysis and Modeling of Fractional Order Model for Hepatitis B at Different Stages
    (Natural Sciences Publishing, 2023) Raza, Ali; Farman, Muhammad; Ahmad, Aqeel; Akgul, Ali; Sultan, Muhammad; Al Bayatti, Hilal
    Fractional operator is used to construct the framework of complex hepatitis B by using Caputo and Caputo Fabrizio fractional order derivative. Examination the uniqueness and stability to test the viability of the fractional order model with the proposed numerical plan as well as analyzes qualitatively. Union of different parts behind iterative approach on account of Fabrizio offers a bounded solution that accomplished required outcomes. The fractional system of differential equations which has four parts, susceptible individuals A(t), acute infected B(t),C(t) is chronic hepatitis and I(t) represents individuals who have retrieve after the infection with a life time freedom. At the end, the impact of the framework parameter on the spread of the ailment are begun to analyze using the numerical simulations. © 2023 NSP Natural Sciences Publishing Cor.
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    Epidemiological Analysis of Symmetry in Transmission of the Ebola Virus with Power Law Kernel
    (Mdpi, 2023) Hasan, Ali; Akgul, Ali; Farman, Muhammad; Chaudhry, Faryal; Sultan, Muhammad; De la sen, Manuel
    This study presents a mathematical model of non-integer order through the fractal fractional Caputo operator to determine the development of Ebola virus infections. To construct the model and conduct analysis, all Ebola virus cases are taken as incidence data. A symmetric approach is utilized for qualitative and quantitative analysis of the fractional order model. Additionally, stability is evaluated, along with the local and global effects of the virus that causes Ebola. Using the fractional order model of Ebola virus infections, the existence and uniqueness of solutions, as well the posedness and biological viability and disease free equilibrium points are confirmed. Many applications of fractional operators in modern mathematics exist, including the intricate and important study of symmetrical systems. Symmetry analysis is a powerful tool that enables the creation of numerical solutions for a given fractional differential equation very methodically. For this, we compare the results with the Caputo derivative operator to understand the dynamic behavior of the disease. The simulation demonstrates how all classes have convergent characteristics and maintain their places over time, reflecting the true behavior of Ebola virus infection. Power law kernel with the two step polynomial Newton method were used. This model seems to be quite strong and capable of reproducing the issue's anticipated theoretical conditions.
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    Impacts of joule heating with Cattaeno- Christove heat flux model in a MHD flow of Erying- Powell fluid on a Riga plate
    (Elsevier, 2023) Shoukat, Zeeshan; Zubair, Muhammad Hashir; Farman, Muhammad; Akguel, Ali; Sultan, Muhammad; Sharipov, Shavkat Safarovich; Botmart, Thongchai
    This article is related to analysing the consequences of joule heating and thermal (hot) radiation on the limit layer stream of a non-Newtonian liquid (Powell-Eyring fluid) while electro transversal magnetic field is present and Cattaneo Christov double diffusion via a convectively heated Riga Plate. The effects of the coefficient of thermophoresis and Brownian motion on joule heating are included in this mathematical model. In this paper, we introduced a new condition namely zero mass flux. A rectangular coordinates system is being employed for the flow equations to get the momentum, energy equations and concentration equations mathematically. By employing a similarity transformation, established (partial differential equations) PDE is reduced into an ordi-nary differential equations ODE. This method is integrated with the Runge-Kutta RK technique to solve this nonlinear ODE numerologically. With Graph, we show different parameters of velocity and temperature etc. Skin friction, with the help of a graph we can also inspect the Nusselt number and Sherwood number in detail. While studying we noticed that the increase of Hartmann number and fluid parameter is caused to increases in fluid velocity and thickness of the boundary layer.
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    Numerical study and dynamics analysis of diabetes mellitus with co-infection of COVID-19 virus by using fractal fractional operator
    (Nature Portfolio, 2024) Farman, Muhammad; Akguel, Ali; Sultan, Muhammad; Riaz, Sidra; Asif, Hira; Agarwal, Praveen; Hassani, Murad Khan
    COVID-19 is linked to diabetes, increasing the likelihood and severity of outcomes due to hyperglycemia, immune system impairment, vascular problems, and comorbidities like hypertension, obesity, and cardiovascular disease, which can lead to catastrophic outcomes. The study presents a novel COVID-19 management approach for diabetic patients using a fractal fractional operator and Mittag-Leffler kernel. It uses the Lipschitz criterion and linear growth to identify the solution singularity and analyzes the global derivative impact, confirming unique solutions and demonstrating the bounded nature of the proposed system. The study examines the impact of COVID-19 on individuals with diabetes, using global stability analysis and quantitative examination of equilibrium states. Sensitivity analysis is conducted using reproductive numbers to determine the disease's status in society and the impact of control strategies, highlighting the importance of understanding epidemic problems and their properties. This study uses two-step Lagrange polynomial to analyze the impact of the fractional operator on a proposed model. Numerical simulations using MATLAB validate the effects of COVID-19 on diabetic patients and allow predictions based on the established theoretical framework, supporting the theoretical findings. This study will help to observe and understand how COVID-19 affects people with diabetes. This will help with control plans in the future to lessen the effects of COVID-19.
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    Yellow virus epidemiological analysis in red chili plants using Mittag-Leffler kernel
    (Elsevier, 2023) Farman, Muhammad; Hasan, Ali; Sultan, Muhammad; Ahmad, Aqeel; Akgul, Ali; Chaudhry, Faryal; Zakarya, Mohammed
    This scientific study investigates to check the dynamical behavior of yellow virus in red chilli with fractional order techniques. While attempts are being made to stop the yellow virus pan-demic, a more infectious yellow virus found in red chilli is developing in many locations. It is crucial to learn how to create strategies that will stop the yellow virus's spread to mimic the propagation of the yellow virus in red chilli plants while maintaining a specific degree of immunity. As a case study, we looked at the possibility of an outbreak in red chilli plants. Recently, novel fractal-fractional operators proposed by Atangana have been widely used to observe the unanticipated elements of a problem. Currently, the illness caused by the yellow virus in red chilli is common and difficult to treat. The inventive operators have been implemented in this structure to observe the influence of vaccination on the yellow virus in the red chilli model using a variety of values for t1 and t2 which are utilized to represent the impact of vaccination. The number of reproductions will determine whether the system is clear of sickness. Using the fractal-fraction Mittag-Leffler operator, we exam-ined the qualitative and quantitative characteristics of the yellow virus in the red chilli model. The results of the fixed point theory are used to apply an improved method for the fractional order model of the yellow virus. Nonlinear analysis was used to assess the stability of the Ulam-Hyres. Numerical simulations are demonstrated to prove the efficiency of the proposed method. The tools employed in this model appear to be quite potent and capable of simulating the expected theoretical conditions in the issue.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).