Yazar "Ahmad, Muhammad Ozair" seçeneğine göre listele

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    A mathematical analysis and simulation for Zika virus model with time fractional derivative
    (Wiley, 2020) Farman, Muhammad; Ahmad, Aqeel; Akgul, Ali; Saleem, Muhammad Umer; Rizwan, Muhammad; Ahmad, Muhammad Ozair
    Zika is a flavivirus that is transmitted to humans either through the bites of infected Aedes mosquitoes or through sexual transmission. Zika has been associated with congenital anomalies, like microcephalus. We developed and analyzed the fractional-order Zika virus model in this paper, considering the vector transmission route with human influence. The model consists of four compartments: susceptible individuals arex(1)(t), infected individuals arex(2)(t),x(3)(t)shows susceptible mosquitos, andx(4)(t)shows the infected mosquitos. The fractional parameter is used to develop the system of complex nonlinear differential equations by using Caputo and Atangana-Baleanu derivative. The stability analysis as well as qualitative analysis of the fractional-order model has been made and verify the non-negative unique solution. Finally, numerical simulations of the model with Caputo and Atangana Baleanu are discussed to present the graphical results for different fractional-order values as well as for the classical model. A comparison has been made to check the accuracy and effectiveness of the developed technique for our obtained results. This investigative research leads to the latest information sector included in the evolution of the Zika virus with the application of fractional analysis in population dynamics.
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    Construction and numerical analysis of a fuzzy non-standard computational method for the solution of an SEIQR model of COVID-19 dynamics
    (Amer Inst Mathematical Sciences-Aims, 2022) Dayan, Fazal; Ahmed, Nauman; Rafiq, Muhammad; Akgul, Ali; Raza, Ali; Ahmad, Muhammad Ozair; Jarad, Fahd
    This current work presents an SEIQR model with fuzzy parameters. The use of fuzzy theory helps us to solve the problems of quantifying uncertainty in the mathematical modeling of diseases. The fuzzy reproduction number and fuzzy equilibrium points have been derived focusing on a model in a specific group of people having a triangular membership function. Moreover, a fuzzy non-standard finite difference (FNSFD) method for the model is developed. The stability of the proposed method is discussed in a fuzzy sense. A numerical verification for the proposed model is presented. The developed FNSFD scheme is a reliable method and preserves all the essential features of a continuous dynamical system.
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    Extraction of soliton for the confirmable time-fractional nonlinear Sobolev-type equations in semiconductor by 06-modal expansion method
    (Elsevier, 2023) Shahzad, Tahir; Ahmad, Muhammad Ozair; Baber, Muhammad Zafarullah; Ahmed, Nauman; Ali, Syed Mansoor; Akguel, Ali; Shar, Muhammad Ali
    The current study deals with the exact solutions of nonlinear confirmable time fractional Sobolev type equations. Such equations have applications in thermodynamics, the flow of fluid through fractured rock. The underlying models are 2D equation of a semi-conductor with heating and Sobolev equation in 2D unbounded domain. These equation are used to describe the different aspects in semi-conductor. The analytical solutions of underlying models is not addressed yet or it is difficult to find. We gain the exact solutions of such models with help of analytical technique namely 06-model expansion method. The abundant families of solutions are obtained by the Jacobi elliptic function and it will give us soliton and solitary wave solutions. So, we extract the different types of solutions such as, dark, bright, singular, combine, periodic and mixed periodic. The unique physical problems are selected from a variety of the solutions that will help the reader for the verification and data experiment. The graphical behavior of the underlying models is represented in the form of 3D, line graphs and their corresponding contours for the various values of the parameters.
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    New applications related to hepatitis C model
    (Amer Inst Mathematical Sciences-Aims, 2022) Ahmed, Nauman; Raza, Ali; Akgul, Ali; Iqbal, Zafar; Rafiq, Muhammad; Ahmad, Muhammad Ozair; Jarad, Fahd
    The main idea of this study is to examine the dynamics of the viral disease, hepatitis C. To this end, the steady states of the hepatitis C virus model are described to investigate the local as well as global stability. It is proved by the standard results that the virus-free equilibrium state is locally asymptotically stable if the value of R-0 is taken less than unity. Similarly, the virus existing state is locally asymptotically stable if R-0 is chosen greater than unity. The Routh-Hurwitz criterion is applied to prove the local stability of the system. Further, the disease-free equilibrium state is globally asymptotically stable if R-0 < 1. The viral disease model is studied after reshaping the integer-order hepatitis C model into the fractal-fractional epidemic illustration. The proposed numerical method attains the fixed points of the model. This fact is described by the simulated graphs. In the end, the conclusion of the manuscript is furnished.
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    Non-polynomial Cubic Spline Method for Three-Dimensional Wave Equation
    (Springer, 2023) Sattar, Rabia; Ahmad, Muhammad Ozair; Pervaiz, Anjum; Ahmed, Nauman; Akgül, Ali
    The scientific community has always been showing deep concern towards partial differential equations (PDEs) and to approximate its numerical solution. This research proposes a non-polynomial cubic spline-based numerical technique for approximating the three-dimensional (3D) wave equation with Dirichlet boundary conditions. The proposed method develops an algebraic scheme for 3D wave equation which can be solved for different spatial and temporal levels. The suggested method provides a three-time level scheme with higher accuracy of order O(h8+ k8+ ?8+ ?2h2+ ?2k2+ ?2?2) by electing appropriate parameter values involved in the spline function. The stability analysis of the suggested numerical technique has been examined and numerical solution of some selected problems are included to exhibit the validity of the proposed method. Numerical results of the test problems are prepared through tables and graphs to demonstrate the effectiveness of the presented work. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.
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    NON-POLYNOMIAL CUBIC SPLINE METHOD USED TO FATHOM SINE GORDON EQUATIONS IN 3+1 DIMENSIONS
    (Vinca Inst Nuclear Sci, 2023) Sattar, Rabia; Ahmad, Muhammad Ozair; Pervaiz, Anjum; Ahmed, Nauman; Akgul, Ali; Abdullaev, Sherzod; Alshaikh, Noorhan
    This study contains an algorithmic solution of the Sine Gordon equation in three space and time dimensional problems. For discretization, the central difference formula is used for the time variable. In contrast, space variable x, y, and z are discretized using the non-polynominal cubic spline functions for each. The proposed scheme brings the accuracy of order O(h(2) + k(2) + sigma(2) + iota(2)h(2) + iota(2)k(2) + iota(2)sigma(2)) by electing suitable parametric values. The paper also discussed the truncation error of the proposed method and obtained the stability analysis. Numerical problems are elucidated by this method and compared to results taken from the literature.
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    On the analytical study of predator-prey model with Holling-II by using the new modified extended direct algebraic technique and its stability analysis
    (Elsevier, 2023) Shahzad, Tahir; Baber, Muhammad Zafarullah; Ahmad, Muhammad Ozair; Ahmed, Nauman; Akgul, Ali; Ali, Syed Mansoor; Ali, Mubasher
    The current study is concerned with a predator-prey model with a functional response of Holling type II that includes prey refuge and diffusion. These types of equations arise in different fields, such as biomathematics , biophysics, polymer rheology, agriculture, thermodynamics, blood flow phenomena, aerodynamics, capacitor theory, electrical circuits, electron-analytical, chemistry, control theory, fitting of experimental data. The underlying model is analytically investigated by a technique, namely a new extended direct algebraic method (NEDAM). The single and combined wave solutions are observed in shock, complex solitary-shock, shock singular, and periodic-singular forms. The rational solutions are also emerged during the derivation. The stability of the model is discussed. There is also a section about unique physical problems. The 3D, 2D, and line graphs are plotted for different values of parameters.
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    Structure preserving numerical scheme for spatio-temporal epidemic model of plant disease dynamics
    (Elsevier, 2021) Azam, Shumaila; Ahmed, Nauman; Akgul, Ali; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Ahmad, Muhammad Ozair; Baleanu, Dumitru
    In this article, an implicit numerical design is formulated for finding the numerical solution of spatiotemporal nonlinear dynamical system with advection. Such type of problems arise in many fields of life sciences, mathematics, physics and engineering. The epidemic model describes the population densities that have some special types of features. These features should be maintained by the numerical design. The proposed scheme, not only solves the nonlinear physical system but also preserves the structure of the state variables. Von-Neumann criteria, M-matrix theory and Taylor's expansion are used for proving some standard results. Basic reproduction number is evaluated and its key role in deciding the stability at the equilibrium points is also investigated. Graphical solutions are also presented against the test problem.