Yazar "Yasin, Muhammad Waqas" 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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    Comparative analysis of numerical with optical soliton solutions of stochastic Gross-Pitaevskii equation in dispersive media
    (Elsevier, 2023) Baber, Muhammad Zafarullah; Ahmed, Nauman; Yasin, Muhammad Waqas; Iqbal, Muhammad Sajid; Akgul, Ali; Riaz, Muhammad Bilal; Rafiq, Muhammad
    This article deals with the stochastic Gross-Pitaevskii equation (SGPE) perturbed with multiplicative time noise. The numerical solutions of the governing model are carried out with the proposed stochastic non-standard finite difference (SNSFD) scheme. The stability of the scheme is proved by using the Von-Neumann criteria and the consistency is shown in the mean square sense. To seek exact solutions, we applied the Sardar subequation (SSE) and modified exponential rational functional (MERF) techniques. The exact solutions are constructed in the form of exponential, hyperbolic, and trigonometric forms. Finally, the comparison of the exact solutions with numerical solutions is drawn in the 3D and line plots for the different values of parameters.
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    Comparisons of Numerical and Solitary Wave Solutions for the Stochastic Reaction-Diffusion Biofilm Model including Quorum Sensing
    (Mdpi, 2024) Baber, Muhammad Zafarullah; Ahmed, Nauman; Yasin, Muhammad Waqas; Iqbal, Muhammad Sajid; Akguel, Ali; Cordero, Alicia; Torregrosa, Juan R.
    This study deals with a stochastic reaction-diffusion biofilm model under quorum sensing. Quorum sensing is a process of communication between cells that permits bacterial communication about cell density and alterations in gene expression. This model produces two results: the bacterial concentration, which over time demonstrates the development and decomposition of the biofilm, and the biofilm bacteria collaboration, which demonstrates the potency of resistance and defense against environmental stimuli. In this study, we investigate numerical solutions and exact solitary wave solutions with the presence of randomness. The finite difference scheme is proposed for the sake of numerical solutions while the generalized Riccati equation mapping method is applied to construct exact solitary wave solutions. The numerical scheme is analyzed by checking consistency and stability. The consistency of the scheme is gained under the mean square sense while the stability condition is gained by the help of the Von Neumann criteria. Exact stochastic solitary wave solutions are constructed in the form of hyperbolic, trigonometric, and rational forms. Some solutions are plots in 3D and 2D form to show dark, bright and solitary wave solutions and the effects of noise as well. Mainly, the numerical results are compared with the exact solitary wave solutions with the help of unique physical problems. The comparison plots are dispatched in three dimensions and line representations as well as by selecting different values of parameters.
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    Numerical investigations of stochastic Newell-Whitehead-Segel equation in (2+1) dimensions
    (World Scientific Publ Co Pte Ltd, 2023) Ahmed, Nauman; Yasin, Muhammad Waqas; Iqbal, Muhammad Sajid; Akgul, Ali; Rafiq, Muhammad; Raza, Ali; Baber, Muhammad Zafarullah
    The stochastic Newell-Whitehead-Segel in (2+1) dimensions is under consideration. It represents the population density or dimensionless temperature and it discusses how stripes appear in temporal and spatial dimensional systems. The Newell-Whitehead-Segel equation (NWSE) has applications in different areas such as ecology, chemical, mechanical, biology and bio-engineering. The important thing is if we see the problem in the two-dimensional (2D) manifold, then the whole 3D picture can be included in the model. The 3D space is embedded compactly in the 2D manifolds. So, 2D problems for the Newell-White-Segel equation are very important because they consider the one, two and three dimensions in it. The numerical solutions of the underlying model have been extracted successfully by two schemes, namely stochastic forward Euler (SFE) and the proposed stochastic nonstandard finite difference (SNSFD) schemes. The existence of the solution is guaranteed by using the contraction mapping principle and Schauder's fixed-point theorem. The consistency of each scheme is proved in the mean square sense. The stability of the schemes is shown by using von Neumann criteria. The SFE scheme is conditionally stable and the SNSFD scheme is unconditionally stable. The efficacy of the proposed methods is depicted through the simulations. The 2D and 3D graphs are plotted for various values of the parameters.
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    Numerical modeling of reaction-diffusion e-epidemic dynamics
    (Springer Heidelberg, 2024) Yasin, Muhammad Waqas; Ashfaq, Syed Muhammad Hamza; Ahmed, Nauman; Raza, Ali; Rafiq, Muhammad; Akguel, Ali
    The objective of this paper is to understand the dynamics of virus spread in a computer network by e-epidemic reaction-diffusion model and applying an implicit finite difference (FD) scheme for a numerical solution. The SIR models are used in studies of epidemiology to predict the behavior of the propagation of biological viruses within the population. We divide the population of computer nodes into three parts i.e. susceptible (may catch the virus), infected 1 (infected but not completely), and infected 2 (completely infected). By using Taylor's series expansion the consistency of the implicit scheme is proved. The unconditional stability of the implicit FD model is proved by using the Von Numan stability analysis. The qualitative analysis of the underlying model is also analyzed such as positivity and boundedness of the model. The numerical stability and bifurcation of is also analyzed. Likewise, identical modeling techniques are adopted to analyze the spread of the virus in digital networks. Because the computer virus behaves in the identical way as the biological virus behaves, this paper emphasizes the significance of diffusion in decreasing the gap between reality and theory, offering a more precise depiction of the spread of the virus within the digital network.
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    Numerical simulations of nonlinear stochastic Newell-Whitehead-Segel equation and its measurable properties
    (Elsevier, 2023) Iqbal, Muhammad Sajid; Yasin, Muhammad Waqas; Ahmed, Nauman; Akgul, Ali; Rafiq, Muhammad; Raza, Ali
    In this article, the stochastic form of the Newell-Whitehead-Segel equation has been investigated. This is a fully nonlinear partial differential equation and has huge applications. The nonlinearity of the underlying problem leads to the fact that one has to do the nonlinear analysis of the problem. So, firstly this article describes the regularity of the solution in the context of existing theory and a new approach has been applied to show the existence of the solution and corresponding explicit a-priori estimates of the Schauder type have been proposed. Secondly, in the next part, we have proposed two numerical schemes for the solution of the underlying problem and both schemes are very fighting for consistency and stability. The obtained numerical results are reliable, time-efficient, and very much adjacent to the exact state of the unknown function. (c) 2022 Elsevier B.V. All rights reserved.
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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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    Pattern Formation and analysis of reaction-diffusion ratio-dependent prey-predator model with harvesting in predator
    (Pergamon-Elsevier Science Ltd, 2024) Ahmed, Nauman; Yasin, Muhammad Waqas; Baleanu, Dumitru; Tintareanu-Mircea, Ovidiu; Iqbal, Muhammad; Akgul, Ali
    A significant degree of complexity to the conventional ecological dynamic is added by studying prey-predator models with harvesting predators. The primary focus of classical models is the link between prey and predator populations, emphasizing their fundamental relationships and biological roles. A complex interaction between biological processes is shown when predator harvesting is combined with prey-predator models. This presents both opportunities and challenges for sustainable resource management. These models help the community to understand how much one can harvest without wiping out the predators or disturbing the balance of the ecosystem. In this study, spatially extended reaction-diffusion prey-predator dynamics with harvesting in predator is analyzed. The unconditionally positivity preserving scheme is applied for the numerical results. Pattern formation in the spatially extended system is also obtained. Various types of patterns like spots, stripes, and holes are observed by using extensive numerical simulations with various parameters. The numerical technique is unconditionally stable, dynamically consistent with the underlying model, preserves the positivity, has bounded behavior, and preserves the all true properties of the continuous model. The underlying model has two equilibrium points and both are successfully obtained with positive behavior for the whole domain. All the theoretical results are verified through the numerical simulations.