Yazar "Shahzad, Muhammad" seçeneğine göre listele

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    Öğe
    Analysis of the fractional diarrhea model with Mittag-Leffler kernel
    (Amer Inst Mathematical Sciences-Aims, 2022) Iqbal, Muhammad Sajid; Ahmed, Nauman; Akgul, Ali; Raza, Ali; Shahzad, Muhammad; Iqbal, Zafar; Rafiq, Muhammad
    In this article, we have introduced the diarrhea disease dynamics in a varying population. For this purpose, a classical model of the viral disease is converted into the fractional-order model by using Atangana-Baleanu fractional-order derivatives in the Caputo sense. The existence and uniqueness of the solutions are investigated by using the contraction mapping principle. Two types of equilibrium points i.e., disease-free and endemic equilibrium are also worked out. The important parameters and the basic reproduction number are also described. Some standard results are established to prove that the disease-free equilibrium state is locally and globally asymptotically stable for the underlying continuous system. It is also shown that the system is locally asymptotically stable at the endemic equilibrium point. The current model is solved by the Mittag-Leffler kernel. The study is closed with constraints on the basic reproduction number R-0 and some concluding remarks.
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    Öğe
    Optimum study of fractional polio model with exponential decay kernel
    (Nature Portfolio, 2024) Iqbal, Muhammad Sajid; Shahzad, Muhammad; Ahmed, Nauman; Akgul, Ali; Ghafoor, Madiha; Hassani, Murad Khan
    This study introduces a fractional order model to investigate the dynamics of polio disease spread, focusing on its significance, unique results, and conclusions. We emphasize the importance of understanding polio transmission dynamics and propose a novel approach using a fractional order model with an exponential decay kernel. Through rigorous analysis, including existence and stability assessment applying the Caputo Fabrizio fractional operator, we derive key insights into the disease dynamics. Our findings reveal distinct disease-free equilibrium (DFE) and endemic equilibrium (EE) points, shedding light on the disease's stability. Furthermore, graphical representations and numerical simulations demonstrate the behavior of the disease under various parameter values, enhancing our understanding of polio transmission dynamics. In conclusion, this study offers valuable insights into the spread of polio and contributes to the broader understanding of infectious disease dynamics.
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    Öğe
    Regularity and wave study of an advection-diffusion-reaction equation
    (Nature Portfolio, 2024) Akgul, Ali; Ahmed, Nauman; Shahzad, Muhammad; Baber, Muhammad Zafarullah; Iqbal, Muhammad Sajid; Chan, Choon Kit
    In this paper, we investigate the optimal conditions to the boundaries where the unique existence of the solutions to an advection-diffusion-reaction equation is secured by applying the contraction mapping theorem from the study of fixed points. Also, we extract, traveling wave solutions of the underlying equation. To this purpose, a new extended direct algebraic method with traveling wave transformation has been used. Achieved soliton solutions are different functions which are hyperbolic, trigonometric, exponential, and some mixed trigonometric functions. These functions show the nature of solitons. Two and three-dimensional plots are drawn using different values of parameters and coefficients for the comparison and behavior of solitons as combined bright-dark, dark, and bright solitons.