Yazar "Azeem, Muhammad" seçeneğine göre listele

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    Analysis of Fractional Order Computer VirusModel with MultipleWays of Infections Potential
    (L and H Scientific Publishing, LLC, 2023) Akgül, Ali; Farman, Muhammad; Akram, Muhammad Mannan; Sajjad, Assad; Azeem, Muhammad
    In this paper, we propose a novel technique for the computer virus epidemic which contains infected external computer effects and removable storage media on the computer viruses. The positivity and boundedness for validation of the model are also discussed. The existence and uniqueness of the system of solutions for the model are made by using fixed point theory and iterative method. Numerical simulation obtained with proposed scheme which shows the impacts of varying the fraction-al-order parameters and the support of the theoretical results. © 2023 L&H Scientific Publishing, LLC. All rights reserved.
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    EPIDEMIOLOGICAL ANALYSIS OF HUMAN LIVER MODEL WITH FRACTIONAL OPERATOR
    (World Scientific Publ Co Pte Ltd, 2023) Azeem, Muhammad; Farman, Muhammad; Abukhaled, Marwan; Nisar, Kottakkaran Sooppy; Akgul, Ali
    This paper will introduce novel techniques for a fractional-order model of the human liver involving the Atangana-Baleanu, Atangana-Toufik, and the Fractal fractional method with the nonsingular kernel. These techniques give more accurate and appropriate results. Existence and uniqueness have been developed with the help of fixed-point theory results. Numerical simulations are done from the developed algorithm of the model to elaborate the effect of fractional values and justify the theoretical results. Such kind of analysis will be useful for further investigation of epidemic diseases, and also provide a better understanding of disease dynamics to overcome the effect of disease in a community.
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    Fractional Order Operator for Symmetric Analysis of Cancer Model on Stem Cells with Chemotherapy
    (Mdpi, 2023) Azeem, Muhammad; Farman, Muhammad; Akgul, Ali; De la Sen, Manuel
    Cancer is dangerous and one of the major diseases affecting normal human life. In this paper, a fractional-order cancer model with stem cells and chemotherapy is analyzed to check the effects of infection in individuals. The model is investigated by the Sumudu transform and a very effective numerical method. The positivity of solutions with the ABC operator of the proposed technique is verified. Fixed point theory is used to derive the existence and uniqueness of the solutions for the fractional order cancer system. Our derived solutions analyze the actual behavior and effect of cancer disease in the human body using different fractional values. Modern mathematical control with the fractional operator has many applications including the complex and crucial study of systems with symmetry. Symmetry analysis is a powerful tool that enables the user to construct numerical solutions of a given fractional differential equation in a fairly systematic way. Such an analysis will provide a better understanding to control the of cancer disease in the human body.
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    FRACTIONAL-ORDER NEWTON-RAPHSON METHOD FOR NONLINEAR EQUATION WITH CONVERGENCE AND STABILITY ANALYSES
    (World Scientific Publ Co Pte Ltd, 2023) Farman, Muhammad; Akgul, Ali; Alshaikh, Noorhan; Azeem, Muhammad; Asad, Jihad
    Fractional-order techniques have many applications in real-life problems nowadays. The utilization of fragmentary math in many parts of science and engineering is wide and somewhat recent. There are various types of subsidiaries that can be valuable in various issues. In this paper, we focus on the effect of this kind of fractional derivative in the search for roots of nonlinear equations and its dependence on the initial estimations. We will check the convergence and stability analyses of the fractional Newton-Raphson (FNR) method for the proposed definitions. We will apply fractional Riemann-Liouville and Caputo-derivatives in the standard Newton root-finding method for different examples and also verify convergence and stability for these problems. Finding a root is very important for nonlinear equations which are used to solve chemical, biological, and engineering problems.