Yazar "Shahzad, Tahir" seçeneğine göre listele

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    Öğe
    Explicit solitary wave structures for the fractional-order Sobolev-type equations and their stability analysis
    (Elsevier, 2024) Shahzad, Tahir; Ahmed, Muhammad Ozair; Baber, Muhammad Zafarullah; Ahmed, Nauman; Akgul, Ali; Abdeljawad, Thabet; Amacha, Inas
    The current research is concerned with solitary wave structures to the time fractional -order Sobolev-type equations. The special types of Sobolev-type equations are under consideration such as the generalized hyperelastic-rod wave (HRW) equation, and Camassa-Holm (CH) equation. These equations occur in several fields, including particularly in quantum field theory, plasma theory, ecology, consolidation of clay and fluid dynamics. The underlying models are investigated analytically by applying two techniques, such as the generalized projective Riccati equation (GPRE) and the modified auxiliary equation (MAE). The gained results are obtained from the different families of solutions such as, including a periodic wave, kink -type wave peakon, a singular wave, and dark solutions. The gained results are denoted as hyperbolic and trigonometric functions. Furthermore, we check that the underlying models are stable using the concept of linearized stability. The propagation behavior of the gained results is displayed in 3D, 2D, and contour visualizations to investigate the influence of various relevant parameters. These results will help the researchers to understand the physical situations.
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    Öğe
    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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    Novel waves structures for the nonclassical Sobolev-type equation in unipolar semiconductor with its stability analysis
    (Nature Portfolio, 2023) Shahzad, Tahir; Ahmed, Muhammad Ozair; Baber, Muhammad Zafarullah; Ahmed, Nauman; Akguel, Ali; El Din, Sayed M.
    In this study, the Sobolev-type equation is considered analytically to investigate the solitary wave solutions. The Sobolev-type equations are found in a broad range of fields, such as ecology, fluid dynamics, soil mechanics, and thermodynamics. There are two novel techniques used to explore the solitary wave structures namely as; generalized Riccati equation mapping and modified auxiliary equation (MAE) methods. The different types of abundant families of solutions in the form of dark soliton, bright soliton, solitary wave solutions, mixed singular soliton, mixed dark-bright soliton, periodic wave, and mixed periodic solutions. The linearized stability of the model has been investigated. Solitons behave differently in different circumstances, and their behaviour can be better understood by building unique physical problems with particular boundary conditions (BCs) and starting conditions (ICs) based on accurate soliton solutions. So, the choice of unique physical problems from various solutions is also carried out. The 3D, line graphs and corresponding contours are drawn with the help of the Mathematica software that explains the physical behavior of the state variable. This information can help the researchers in their understanding of the physical conditions.
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    Öğe
    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.