Yazar "Ali, Syed Mansoor" seçeneğine göre listele

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    Abundant soliton solution for the time-fractional stochastic Gray-Scot model under the influence of noise and M-truncated derivative
    (Springer, 2024) Baber, Muhammad Zafarullah; Ahmed, Nauman; Yasin, Muhammad Waqas; Ali, Syed Mansoor; Ali, Mubasher; Akgul, Ali; Hassani, Murad Khan
    In this study, we investigate the abundant soliton solutions for the time-fractional stochastic Gray-Scot (TFSGS) model analytically. The Gray-Scot model is considered under the influence of M-truncated derivative and multiplicative time noise. This is a reaction-diffusion chemical concentration model that explains the irreversible chemical reaction process. The M-truncated derivative is applied for the fractional version while Brownian motion is taken in the sense of time noise. The novel mathematical technique is used to obtain the abundant families of soliton solutions. These solutions are explored in the form of shock, complicated solitary-shock, shock-singular, and periodic-singular types of single and combination wave structures. During the derivation, the rational solutions also appear. Moreover, we use MATHEMATICA 11.1 tools to plot our solutions and exhibit several three-dimensional, two-dimensional, and their corresponding contour graphs to show the fractional derivative and Brownian motion impact on the soliton solutions of the TFSGS model. We show that the TFDGS model solutions are stabilized at around zero by the multiplicative Brownian motion. These wave solutions represent the chemical concentrations of the reactants. The TFDGS model is considered to find the exact solitsary wave solutions under the random environment.The new MEDA method is used to obtain the different form of solutions.The different graphical behaviour are drawn to show the effects of noise and fractional derivatives.
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    Analysis of multi-wave solitary solutions of (2+1)-dimensional coupled system of Boiti-Leon-Pempinelli
    (Nature Portfolio, 2024) Ghazanfar, Sidra; Ahmed, Nauman; Iqbal, Muhammad Sajid; Ali, Syed Mansoor; Akgul, Ali; Muhammad, Shah; Ali, Mubasher
    This work examines the (2+1)-dimensional Boiti-Leon-Pempinelli model, which finds its use in hydrodynamics. This model explains how water waves vary over time in hydrodynamics. We provide new explicit solutions to the generalized (2+1)-dimensional Boiti-Leon-Pempinelli equation by applying the Sardar sub-equation technique. This method is shown to be a reliable and practical tool for solving nonlinear wave equations. Furthermore, different types of solitary wave solutions are constructed: w-shaped, breather waved, chirped, dark, bright, kink, unique, periodic, and more. The results obtained with the variable coefficient Boiti-Leon-Pempinelli equation are stable and different from previous methods. As compared to their constant-coefficient counterparts, the variable-coefficient models are more general here. In the current work, the problem is solved using the Sardar Sub-problem Technique to produce distinct soliton solutions with parameters. Plotting these graphs of the solutions will help you better comprehend the model. The outcomes demonstrate how well the method works to solve nonlinear partial differential equations, which are common in mathematical physics.With the help of this method, we may examine a variety of solutions from significant physical perspectives.
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    Analytical study of reaction diffusion Lengyel-Epstein system by generalized Riccati equation mapping method
    (Nature Portfolio, 2023) Ahmed, Nauman; Baber, Muhammad Z.; Iqbal, Muhammad Sajid; Annum, Amina; Ali, Syed Mansoor; Ali, Mubasher; Akgul, Ali
    In this study, the Lengyel-Epstein system is under investigation analytically. This is the reaction-diffusion system leading to the concentration of the inhibitor chlorite and the activator iodide, respectively. These concentrations of the inhibitor chlorite and the activator iodide are shown in the form of wave solutions. This is a reactionaeuro diffusion model which considered for the first time analytically to explore the different abundant families of solitary wave structures. These exact solitary wave solutions are obtained by applying the generalized Riccati equation mapping method. The single and combined wave solutions are observed in shock, complex solitary-shock, shock singular, and periodic-singular forms. The rational solutions also emerged during the derivation. In the Lengyel-Epstein system, solitary waves can propagate at various rates. The harmony of the system's diffusive and reactive effects frequently governs the speed of a single wave. Solitary waves can move at a variety of speeds depending on the factors and reaction kinetics. To show their physical behavior, the 3D and their corresponding contour plots are drawn for the different values of constants.
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    Computational aspects of an epidemic model involving stochastic partial differential equations
    (World Scientific Publ Co Pte Ltd, 2023) Ahmed, Nauman; Yasin, Muhammad W.; Ali, Syed Mansoor; Akguel, Ali; Raza, Ali; Rafiq, Muhammad; Shar, Muhammad Ali
    This paper deals with the study of the reaction-diffusion epidemic model perturbed with time noise. It has various applications such as disease in population models of humans, wildlife, and many others. The stochastic SIR model is numerically investigated with the proposed stochastic backward Euler scheme and proposed stochastic implicit finite difference (IFD) scheme. The stability of the proposed methods is shown with Von Neumann criteria and both schemes are unconditionally stable. Both schemes are consistent with systems of the equations in the mean square sense. The numerical solution obtained by the proposed stochastic backward Euler scheme and solutions converges towards an equilibrium but it has negative and divergent behavior for some values. The numerical solution gained by the proposed IFD scheme preserves the positivity and also solutions converge towards endemic and disease-free equilibrium. We have used two problems to check our findings. The graphical behavior of the stochastic SIR model is much adjacent to the classical SIR epidemic model when noise strength approaches zero. The three-dimensional plots of the susceptible and infected individuals are drawn for two cases of endemic equilibrium and disease-free equilibriums. The results show the efficacy of the proposed stochastic IFD scheme.
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    Exact and solitary wave structure of the tumor cell proliferation with LQ model of three dimensional PDE by newly extended direct algebraic method
    (Aip Publishing, 2023) Ghazanfar, Sidra; Ahmed, Nauman; Ali, Syed Mansoor; Iqbal, Muhammad Sajid; Akgul, Ali; Shar, Muhammad Ali; Bariq, Abdul
    An essential stage in the spread of cancer is the entry of malignant cells into the bloodstream. The fundamental mechanism of cancer cell intravasation is still completely unclear, despite substantial advancements in observing tumor cell mobility in vivo. By creating therapeutic methods in conjunction with control engineering or by using the models for simulations and treatment process evaluation, tumor growth models have established themselves as a crucial instrument for producing an engineering backdrop for cancer therapy. Because tumor growth is a highly complex process, mathematical modeling has been essential for describing it because a carefully crafted tumor growth model constantly describes the measurements and the physiological processes of the tumors. This article discusses the exact and solitary wave behavior of a tumor cell with a three-dimensional linear-quadratic model. Exact solutions have been discussed in detail using the newly extended direct algebraic method, which presents a variety of answers to this issue based on the conditions applied. This article also illustrates its graphical behavior with surface and contour plots of several solitons.
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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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    Investigating the impact of stochasticity on HIV infection dynamics in CD4+T cells using a reaction-diffusion model
    (Nature Portfolio, 2024) Ahmed, Nauman; Yasin, Muhammad W.; Ali, Syed Mansoor; Akgul, Ali; Raza, Ali; Rafiq, Muhammad; Muhammad, Shah
    The disease dynamics affect the human life. When one person is affected with a disease and if it is not treated well, it can weaken the immune system of the body. Human Immunodeficiency Virus (HIV) is a virus that attacks the immune system, of the body which is the defense line against diseases. If it is not treated well then HIV progresses to its advanced stages and it is known as Acquired Immunodeficiency Syndrome (AIDS). HIV is typically a disease that can transferred from one person to another in several ways such as through blood, breastfeeding, sharing needles or syringes, and many others. So, the need of the hour is to consider such important disease dynamics and that will help mankind to save them from such severe disease. For the said purpose the reaction-diffusion HIV CD4+ T cell model with drug therapy under the stochastic environment is considered. The underlying model is numerically investigated with two time-efficient schemes and the effects of various parameters used in the model are analyzed and explained in a real-life scenario. Additionally, the obtained results will help the decision-makers to avoid such diseases. The random version of the HIV model is numerically investigated under the influence of time noise in Ito<^> sense. The proposed stochastic backward Euler (SBE) scheme and proposed stochastic Implicit finite difference (SIFD) scheme are developed for the computational study of the underlying model. The consistency of the schemes is proven in the mean square sense and the given system of equations is compatible with both schemes. The stability analysis proves that both schemes and schemes are unconditionally stable. The given system of equations has two equilibria, one is disease-free equilibrium (DFE) and the other is endemic equilibrium. The simulations are drawn for the different values of the parameters. The proposed SBE scheme showed the convergent behavior towards the equilibria for the given values of the parameters but also showed negative behavior that is not biological. The proposed SIFD scheme showed better results as compared with the stochastic SBE scheme. This scheme has convergent and positive behavior towards the equilibria points for the given values of the parameters. The effect of various parameters is also analyzed. Simulations are drawn to evaluate the efficacy of the schemes.
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    Numerical study of diffusive fish farm system under time noise
    (Nature Portfolio, 2024) Yasin, Muhammad Waqas; Ahmed, Nauman; Saeed, Jawaria; Baber, Muhammad Zafarullah; Ali, Syed Mansoor; Akgul, Ali; Muhammad, Shah
    In the current study, the fish farm model perturbed with time white noise is numerically examined. This model contains fish and mussel populations with external food supplied. The main aim of this work is to develop time-efficient numerical schemes for such models that preserve the dynamical properties. The stochastic backward Euler (SBE) and stochastic Implicit finite difference (SIFD) schemes are designed for the computational results. In the mean square sense, both schemes are consistent with the underlying model and schemes are von Neumann stable. The underlying model has various equilibria points and all these points are successfully gained by the SIFD scheme. The SIFD scheme showed positive and convergent behavior for the given values of the parameter. As the underlying model is a population model and its solution can attain minimum value zero, so a solution that can attain value less than zero is not biologically possible. So, the numerical solution obtained by the stochastic backward Euler is negative and divergent solution and it is not a biological phenomenon that is useless in such dynamical systems. The graphical behaviors of the system show that external nutrient supply is the important factor that controls the dynamics of the given model. The three-dimensional results are drawn for the various choices of the parameters.
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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.