Yazar "Chaudhry, Faryal" seçeneğine göre listele

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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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    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/).