Yazar "Iqbal, Muhammad Sajid" seçeneğine göre listele

Listeleniyor 1 - 20 / 26
  • [ X ]
    Öğe
    A fractal fractional model for computer virus dynamics
    (Pergamon-Elsevier Science Ltd, 2021) Akgul, Ali; Fatima, Umbreen; Iqbal, Muhammad Sajid; Ahmed, Nauman; Raza, Ali; Iqbal, Zafar; Rafiq, Muhammad
    The gist behind this study is to extend the classical computer virus model into fractal fractional model and subsequently to solve the model by Atangana-Toufik method. This method solve nonlinear model under consideration very efficiently. We use the Mittag-Leffler kernels on the proposed model. Atangana-Baleanu integral operator is used to solve the set of fractal-fractional expressions. In this model, three types of equilibrium points are described i.e trivial, virus free and virus existing points. These fixed points are used to establish some standard results to discuss the stability of the system by calculating the Jacobian matrices at these points. Routh-Hurwitz criteria is used to verify that the system is locally asymptotically stable at all the steady states. The emphatic role of the basic reproduction number R-0 is also brought into lime light for stability analysis. Sensitivity analysis of R-0 is also discussed. Optimal existence and uniqueness of the solution is the nucleus of this study. Computer simulations and patterns and graphical patterns illustrate reliability and productiveness of the proposed method. (C) 2021 Elsevier Ltd. All rights reserved.
  • [ X ]
    Öğe
    A Nonlinear Structure of a Chemical Reaction Model and Numerical Modeling with the New Aspect of Existence and Uniqueness
    (Mdpi, 2023) Shaikh, Tahira Sumbal; Akgul, Ali; Rehman, Muhammad Aziz-ur; Ahmed, Nauman; Iqbal, Muhammad Sajid; Shahid, Naveed; Rafiq, Muhammad
    In this article, a nonlinear autocatalytic chemical reaction glycolysis model with the appearance of advection and diffusion is proposed. The occurrence and unicity of the solutions in Banach spaces are investigated. The solutions to these types of models are obtained by the optimization of the closed and convex subsets of the function space. Explicit estimates of the solutions for the admissible auxiliary data are formulated. An elegant numerical scheme is designed for an autocatalytic chemical reaction model, that is, the glycolysis model. The fundamental traits of the prescribed numerical method, for instance, the positivity, consistency, stability, etc., are also verified. The authenticity of the proposed scheme is ensured by comparing it with two extensively used numerical techniques. A numerical example is presented to observe the graphical behavior of the continuous system by constructing the numerical algorithm. The comparison depicts that the projected numerical design is more productive as compared to the other two schemes, as it holds all the important properties of the continuous model.
  • [ X ]
    Öğe
    Acoustic wave structures for the confirmable time-fractional Westervelt equation in ultrasound imaging
    (Elsevier, 2023) Shaikh, Tahira Sumbal; Baber, Muhammad Zafarullah; Ahmed, Nauman; Iqbal, Muhammad Sajid; Akgul, Ali; El Din, Sayed M.
    In this study, the acoustic nonlinear equation namely the confirmable time-fractional Westervelt equation is under consideration analytically. This equation is applicable in the wave propagation of sound and high amplitude in medical imaging and therapy. The different types of wave structures are constructed for the confirmable time-fractional Westervelt equation by using two different techniques namely as, the modified exponential rational functional method and the modified G'/G(2)-model expansion method. With the help of these two techniques, we gain the different hyperbolic, exponential, periodic, and plane wave function solutions. Additionally, to show the graphical behavior of the wave structure, the 3D, 2D, and their corresponding contour representations are drawn by the different choices of parameters.
  • [ X ]
    Öğe
    Analysis and Modelling of HIV/AIDS Model with Fractional Order Parameter Estimation
    (Natural Sciences Publishing, 2022) Farman, Muhammad; Raza, Ali; Akgul, Ali; Saleem, Muhammad Umer; Ahmad, Aqeel; Iqbal, Muhammad Sajid
    In this paper, nonlinear fractional order HIV/AIDS mathematical model is discussed epidemic problems for the complex transmission of the disease. It is accepted that susceptible wind up contaminated by means of sexual contacts with infective eventually create AIDS. The point of this task was to amend transmission models recently created to represent HIV transmission and AIDS related mortality. The Caputo-Fabrizio fractional derivative operator of order ? ? (0,1) is used to obtain fractional differential equations structure. The stability fractional order model was developed and the unique non-negative solution was tested. The numerical simulations are performed using an iterative technique. Some new results are being viewed with the help of Sumudo transform. Nonetheless, according to Banach, the related findings are given nonlinear functional analysis and fixed point theory. However, mathematical simulations are also acknowledged to evaluate the impact of the model’s parameter by decreasing the fractional values and showing the effect of the b fractional parameter on our obtained solutions. The impact of various parameters is represented graphically. © 2022. NSP Natural Sciences Publishing Cor.
  • [ X ]
    Öğe
    Analysis of a Modified System of Infectious Disease in a Closed and Convex Subset of a Function Space with Numerical Study
    (Mdpi, 2023) Shaikh, Tahira Sumbal; Akgul, Ali; Rehman, Muhammad Aziz ur; Ahmed, Nauman; Iqbal, Muhammad Sajid; Shahid, Naveed; Rafiq, Muhammad
    In this article, the transmission dynamical model of the deadly infectious disease namedEbola is investigated. This disease identified in the Democratic Republic of Congo (DRC) and Sudan(now South Sudan) and was identified in 1976. The novelty of the model under discussion is theinclusion of advection and diffusion in each compartmental equation. The addition of these two termsmakes the model more general. Similar to a simple population dynamic system, the prescribed modelalso has two equilibrium points and an important threshold, known as the basic reproductive number.The current work comprises the existence and uniqueness of the solution, the numerical analysis ofthe model, and finally, the graphical simulations. In the section on the existence and uniqueness ofthe solutions, the optimal existence is assessed in a closed and convex subset of function space. Forthe numerical study, a nonstandard finite difference (NSFD) scheme is adopted to approximate thesolution of the continuous mathematical model. The main reason for the adoption of this technique isdelineated in the form of the positivity of the state variables, which is necessary for any populationmodel. The positivity of the applied scheme is verified by the concept of M-matrices. Since thenumerical method gives a discrete system of difference equations corresponding to a continuoussystem, some other relevant properties are also needed to describe it. In this respect, the consistencyand stability of the designed technique are corroborated by using Taylor's series expansion and Von Neumann's stability criteria, respectively. To authenticate the proposed NSFD method, two other illustrious techniques are applied for the sake of comparison. In the end, numerical simulations are also performed that show the efficiency of the prescribed technique, while the existing techniques fail to do so.
  • [ X ]
    Öğe
    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.
  • [ X ]
    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.
  • [ X ]
    Öğe
    Analysis of the fractional polio model with the Mittag-Leffler kernels
    (Elsevier, 2023) Iqbal, Muhammad Sajid; Ahmed, Nauman; Akgul, Ali; Satti, Ammad Mehmood; Iqbal, Zafar; Raza, Ali; Rafiq, Muhammad
    This article investigates the transmission of polio-virus disease in the human population. The classical model is considered for studying fatal disease. First of all, the model is converted into the fractal fractional epidemic model. Then, the existence of the solution for the said model is ensured with the help of the fixed point theory. Points of equilibria for the model are worked out. The basic reproduction number is described and its role in the disease communication and sta-bility of the model is examined by some standard results. Simulated graphs are also plotted to sup-port the pre-results and claims. Lastly, the findings of the study are presented.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
  • [ X ]
    Öğe
    Analytical investigation of space–time shifted nonlocal stochastic Sasa–Satsuma equation using the enhanced modified extended tanh-expansion method for stochastic solitary waves Solutions
    (Elsevier B.V., 2024) Manzoor, Zuha; Ashraf, Farrah; Iqbal, Muhammad Sajid; Akgül, Ali; Misro, Md Yushalify
    In this paper, discover exact solutions of the space–time shifted nonlocal stochastic Sasa–Satsuma equations using the enhanced modified extended tanh-expansion method. This method is a sophisticated mathematical approach for analytical and approximate solution of a nonlinear partial differential equations. The space–time shifted nonlocal stochastic Sasa–Satsuma equations define the behavior of two complex-valued functions, u and v, in a nonlinear system. These equations are complicated to solve analytically because they contain a number of components that describe space–time shifting, nonlocal interactions, and stochastic problems. To increase reliability and effectiveness of the solutions, this method couples the extended tanh-function method with an enhanced method. In order to demonstrate how white noise affects the solutions to the space–time shifted nonlocal stochastic Sasa–Satsuma equations, we also use Matlab to create 3D surfaces and contour graphs of exact solutions. © 2024 The Author(s)
  • [ X ]
    Öğe
    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.
  • [ X ]
    Öğe
    Analyzing multiplicative noise effects on stochastic dynamical ?4 equation using the new extended direct algebraic method
    (Elsevier, 2024) Manzoor, Zuha; Iqbal, Muhammad Sajid; Omer, Nader; Zakarya, Mohammed; Kanan, Mohammad; Akgul, Ali; Hussain, Shabbir
    The stochastic dynamical phi(4) equation is obtained by adding a multiplicative noise term to the classical phi(4) equation. The noise term represents the random fluctuations that are present in the system and is modeled by a Wiener process. The stochastic dynamical phi(4) equation is a powerful tool for modeling the behavior of complex systems that exhibit randomness and nonlinearity. It has a wide range of applications in physics, chemistry, biology, and finance. Our goal of this paper is to use the new extended direct algebraic method to find the stochastic traveling wave solutions of the dynamical phi(4) equation. We explore the new trigonometric, hyperbolic, and rational functions using the new extended direct algebraic method. Furthermore, we use Matlab to plot 3D surfaces of exact solutions to show how multiplicative noise affects the solutions to the stochastic dynamical phi(4) equation.
  • [ X ]
    Öğe
    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.
  • [ X ]
    Öğe
    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.
  • [ X ]
    Öğe
    Dynamical behavior of cancer cell densities in two dimensional domain by the representation theory of solitons
    (Elsevier, 2023) Iqbal, Muhammad Sajid; Ahmed, Nauman; Naeem, Rishi; Akgul, Ali; Razzaque, Abdul; Inc, Mustafa; Khurshid, Hina
    This article analyzes the mathematical model which is described by the nonlinear partial differential equation governing the density of cancer cells at any position (x, y) in the open bounded subset of the plane at any time t. This is a two-dimensional model that describes the dynamics of cancer cells under radiotherapy and its comparison with the one in the absence of radiation effects. The 06-model expansion method has been used to find the exact solutions of the underlying problem. The simulation of obtained results have also been argued.(c) 2023 Elsevier B.V. All rights reserved.
  • [ X ]
    Öğe
    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.
  • [ X ]
    Öğe
    Imaging Ultrasound Propagation Using the Westervelt Equation by the Generalized Kudryashov and Modified Kudryashov Methods
    (Mdpi, 2022) Ghazanfar, Sidra; Ahmed, Nauman; Iqbal, Muhammad Sajid; Akgul, Ali; Bayram, Mustafa; De la Sen, Manuel
    This article deals with the study of ultrasound propagation, which propagates the mechanical vibration of the molecules or of the particles of a material. It measures the speed of sound in air. For this reason, the third-order non-linear model of the Westervelt equation was chosen to be studied, as the solutions to such problems have much importance for physical purposes. In this article, we discuss the exact solitary wave solutions of the third-order non-linear model of the Westervelt equation for an acoustic pressure p representing the equation of ultrasound with high intensity, as used in acoustic tomography. Moreover, the non-linear coefficient B / A (being a part of space-dependent coefficient K), has also been investigated in this literature. This problem is solved using the Generalized Kudryashov method along with a comparison of the Modified Kudryashov method. All of the solutions have been discussed with both surface and contour plots, which shows the behavior of the solution. The images are prepared in a well-established way, showing the production of tissues inside the human body.
  • [ X ]
    Öğe
    Investigation of solitary wave structures for the stochastic Nizhnik-Novikov-Veselov (SNNV) system (vol 48, 106389, 2023)
    (Elsevier, 2023) Shaikh, Tahira Sumbal; Baber, Muhammad Zafarullah; Ahmed, Nauman; Iqbal, Muhammad Sajid; Akgul, Ali; El Din, Sayed M.
    [Abstract Not Available]
  • [ X ]
    Öğe
    Investigation of soliton structures for dispersion, dissipation, and reaction time-fractional KdV-burgers-Fisher equation with the noise effect
    (Taylor & Francis Inc, 2024) Ahmed, Nauman; Baber, Muhammad Z.; Iqbal, Muhammad Sajid; Akguel, Ali; Rafiq, Muhammad; Raza, Ali; Chowdhury, Mohammad Showkat Rahim
    In this manuscript, the soliton structures for the time-fractional KdV-Burgers-Fisher equation with the effect of noise are investigated analytically. This is the dispersion-dissipation-reaction model. The third- and fifth-order time-fractional stochastic KdV-Burgers-Fisher equations are under consideration. These wave structures are constructed with the help of an extended generalized Riccati equation mapping method (EGREM). This method is a combined form of the $G'/G$G '/G expansion method with the generalized Riccati equation mapping method, and it will give the different forms of wave structures like shock, singular, combo, hyperbolic, trigonometric, mixed trigonometric, and rational solutions. These techniques are used symbolically with computational tools like Mathematica to demonstrate the efficiency and simplicity of the proposed strategy. Additionally, with the various relevant parameter values, the sketches of some solutions in the form of 3D and contour representations for the purpose of comprehending physical processes are drawn. These sketches clearly show the random behavior of these wave structures that are appearing in dispersion, dissipation, and reaction concentrations of these mathematical models.
  • [ X ]
    Öğe
    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.
  • [ X ]
    Öğe
    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.