Yazar "Baber, Muhammad Zafarullah" seçeneğine göre listele

Listeleniyor 1 - 17 / 17
  • [ X ]
    Öğe
    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.
  • [ 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
    Breather, lump, M-shape and other interaction for the Poisson-Nernst-Planck equation in biological membranes
    (Springer, 2024) Ceesay, Baboucarr; Ahmed, Nauman; Baber, Muhammad Zafarullah; Akguel, Ali
    This paper investigates a novel method for exploring soliton behavior in ion transport across biological membranes. This study uses the Hirota bilinear transformation technique together with the Poisson-Nernst-Planck equation. A thorough grasp of ion transport dynamics is crucial in many different scientific fields since biological membranes are important in controlling the movement of ions within cells. By extending the standard equation, the suggested methodology offers a more thorough framework for examining ion transport processes. We examine a variety of ion-acoustic wave structures using the Hirota bilinear transformation technique. The different forms of solitons are obtained including breather waves, lump waves, mixed-type waves, periodic cross-kink waves, M-shaped rational waves, M-shaped rational wave solutions with one kink, and M-shaped rational waves with two kinks. It is evident from these numerous wave shapes that ion transport inside biological membranes is highly relevant, and they provide important insights that may have an impact on various scientific disciplines, medication development, and other areas. This extensive approach helps scholars dig deeper into the complexity of ion transport, illuminating the complicated mechanisms driving this essential biological function. Additionally, to show the physical interpretations of these solutions we construct the 3D and their corresponding contour plots by choosing the different values of constants. So, these solutions give us the better physical behaviors.
  • [ 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 study of groundwater systems using the new auxiliary equation method
    (Elsevier, 2024) Shahid, Naveed; Baber, Muhammad Zafarullah; Shaikh, Tahira Sumbal; Iqbal, Gulshan; Ahmed, Nauman; Akgul, Ali; De la Sen, Manuel
    In this research, the exact solitary wave solutions to the non-linear problem of underground water levels are found. This study examines the transport of solutes in groundwater systems with variable density flow. The mathematical equation that is used to explain how groundwater moves through an aquifer is known as the groundwater flow equation and is used in hydrogeology. The auxiliary equation method is used to gain the analytical solutions to the underlying model equation. These solutions are gained in the form of hyperbolic, trigonometric, exponential, and rational function solutions. Mathematica generates two-dimensional and threedimensional graphs with suitable parameter values. The resulting solutions are also useful for researching wave interactions in several novel structures.
  • [ X ]
    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.
  • [ X ]
    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.
  • [ X ]
    Öğe
    Investigation of solitary wave structures for the stochastic Nizhnik-Novikov-Veselov (SNNV) system
    (Elsevier, 2023) Shaikh, Tahira Sumbal; Baber, Muhammad Zafarullah; Ahmed, Nauman; Sajid, Muhammad; Akgul, Ali; El Din, Sayed M.
    The current study deals with the stochastic Nizhnik-Novikov-Veselov (SNNV) system analytically under the multiplicative noise effect. The Nizhnik-Novikov-Veselov equation is an extension of the KdV equation with applications in shallow-water waves, ionic acoustic waves in plasma, long internal waves in density-stratified oceans, and sound waves on crystal networks. The stochastic wave structures are constructed with the help of the Sardar subequation method. The different solutions are extracted which are in the form of solitons and solitary wave structures in the noise effect. Additionally, the stochastic behavior appears in the 3-dim, 2-dim, and their corresponding contour representations by the various selection of parameters.
  • [ 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
    Modelling Symmetric Ion-Acoustic Wave Structures for the BBMPB Equation in Fluid Ions Using Hirota's Bilinear Technique
    (Mdpi, 2023) Ceesay, Baboucarr; Baber, Muhammad Zafarullah; Ahmed, Nauman; Akgül, Ali; Cordero, Alicia; Torregrosa, Juan R.
    This paper investigates the ion-acoustic wave structures in fluid ions for the Benjamin-Bona-Mahony-Peregrine-Burgers (BBMPB) equation. The various types of wave structures are extracted including the three-wave hypothesis, breather wave, lump periodic, mixed-type wave, periodic cross-kink, cross-kink rational wave, M-shaped rational wave, M-shaped rational wave solution with one kink wave, and M-shaped rational wave with two kink wave solutions. The Hirota bilinear transformation is a powerful tool that allows us to accurately find solutions and predict the behaviour of these wave structures. Through our analysis, we gain a better understanding of the complex dynamics of ion-acoustic waves and their potential applications in various fields. Moreover, our findings contribute to the ongoing research in plasma physics that utilize ion-acoustic wave phenomena. To show the physical behaviour of the solutions, some 3D plots and their respective contour level are shown, choosing different values of the parameters.
  • [ X ]
    Öğe
    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.
  • [ 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 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.
  • [ X ]
    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.
  • [ X ]
    Öğe
    On the Soliton Solutions for the Stochastic Konno-Oono System in Magnetic Field with the Presence of Noise
    (Mdpi, 2023) Shaikh, Tahira Sumbal; Baber, Muhammad Zafarullah; Ahmed, Nauman; Shahid, Naveed; Akgul, Ali; de la Sen, Manuel
    In this study, we consider the stochastic Konno-Oono system to investigate the soliton solutions under the multiplicative sense. The multiplicative noise is considered firstly in the Stratonovich sense and secondly in the Ito sense. Applications of the Konno-Oono system include current-fed strings interacting with an external magnetic field. The F-expansion method is used to find the different types of soliton solutions in the form of dark, singular, complex dark, combo, solitary, periodic, mixed periodic, and rational functions. These solutions are applicable in the magnetic field when we study it at the micro level. Additionally, the absolute, real, and imaginary physical representations in three dimensions and the corresponding contour plots of some solutions are drawn in the sense of noise by the different choices of parameters.
  • [ X ]
    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.