Jamshad Ahmad

Jamshad Ahmad
University of Gujrat | UOG · Department of Mathematics

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138
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Publications

Publications (138)
Article
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This paper examines the fractional Kraenkel-Manna-Merle (KMM) system, which models the behavior of a nonlinear ultrashort wave pulse in non-conductive saturated ferromagnetic materials. The primary contribution of this paper is a thorough dynamical analysis of the model in non-conductive saturated ferromagnetic materials, employing the beta derivat...
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The nonlinear conformable time-fractional Symmetric Regularized Long Wave (SRLW) equation is a significant model in physics, particularly for describing ion acoustic and space charge waves with weak nonlinearity. In this study, we apply the modified Sardar sub equation method and the modified extended auxiliary equation method to solve the SRLW equ...
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In this study, we use analytical algorithms, specifically the auxiliary equation (AE) approach, the improved F-expansion method, and the modified Sardar sub-equation (MSSE) method to investigate complex wave structures for plentiful solutions associated with the fractional perturbed Gerdjikov-Ivanov (PGI) model with the M-fractional operator. The i...
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The primary aim of this paper is to investigate the dynamic behavior of generalized nonlinear fractional Tzitzéica-type equations and to derive optical soliton solutions. To achieve this goal, we employ the modified Khater method, focusing on obtaining solitary wave solutions for generalized fractional Tzitzéica-type (TT) equations. Through this ap...
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In this work, the Hirota bilinear symbolic computational method along with test functions and the generalized exponential rational function method are capitalized to secure soliton and lump solutions to the Sharma–Tasso–Olver–Burgers equation. Several novel soliton solutions are observed in unique patterns such as periodic, exponential, hyperbolic,...
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In this paper, the stochastic fractional Radhakrishnan– Kundu–Lakshmanan equation (SFRKLE) with Kerr law nonlinearity is studied, which is one of the important mathematical model in nonlinear optics. The main purpose of this study is to obtain the different kinds of soliton solutions of SFRKLE with Kerr law nonlinearity that are absent in the liter...
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In this article, we investigate the behavior of unstable NLSE and the modify unstable NLSE to derive solitonic solutions. These equations describe the time evolution of disturbances in an unstable medium. We employ the amended extended tangent hyperbolic function method to solve these equations, yielding precise solutions that are simple, rational,...
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In this paper, we explore the intricate dynamics of ultrashort light pulses using a sophisticated higher-order nonlinear Schrödinger equation (NLSE). This equation incorporates third-order dispersion (3OD), fourth-order dispersion (4OD), and cubic-quintic nonlinearity (CQNL) terms, providing a nuanced perspective on how light pulses propagate throu...
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This article explores a noteworthy nonlinear model, namely the truncated M-fractional resonant nonlinear Schrödinger equation (RNLSE), incorporating a Kerr law nonlinearity. Various nonlinear phenomena in research domains like nonlinear optics, the atmospheric theory of deep water waves, quantum mechanics, plasma physics, and fluid dynamics can be...
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This study explores optical soliton solutions within the framework of the Caudrey–Dodd–Gibbon equation (CDGE) and the (1+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}...
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In nature, complex phenomena can be described by the system of nonlinear partial differential equations. The solitons are significant nonlinear phenomenon in optics that appears when the nonlinearity precisely balances the dispersion. The key objective of this research is to investigate a range of optical soliton solutions for the nonlinear Biswas–...
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The primary objective of this study is to extract nonlinear wave patterns from the (4+1)-dimensional Boiti–Leon–Manna–Pempinelli (4D-BLMP) equation, considering both constant and time-dependent coefficients, which is used widely to describe the incompressible fluid. By employing the amended extended tanh-function method, we successfully obtained in...
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This research extensively investigates the fractional coupled Konno–Oono model, a prevalent framework in diverse scientific and engineering disciplines. The primary objective is to unravel the intricate dynamics embedded in this model. We adeptly convert partial differential equations into ordinary differential equation by applying appropriate tran...
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This article examines the nonlinear (2+1) complex conformable time fractional nonlinear Schrödinger equation and the soliton solutions that may be found by using the improved F-expansion method. Many novel solutions of concatenated model such as periodic wave, dark soliton, singular, hyperbolic, trigonometric and rational wave soliton solutions are...
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In this manuscript, we employ the unified method and the Sardar subequation method to systematically analyze various wave structures within the (3+1)-dimensional extended quantum nonlinear Zakharov–Kuznetsov equation, incorporating test function approaches. The equation, integral to understanding the intricate dynamics of quantum plasma in diverse...
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This article investigates the truncated time M-fractional paraxial wave equation. This model is frequently used to depict the activation of waves in utterly different physical frameworks, such as quantum mechanics and optics. Two trustworthy methodologies, the improved F-expansion and modified exponent function method, are used to obtain the differ...
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This study explores solutions for a mathematical equation called the time-space fractional phi-four equation using two methods: the Sardar-subequation method and the modified extended auxiliary equation method. The phi-four equation is connected to the Klein–Gordon model and is important in different scientific areas like biology and nuclear physic...
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In this study, we investigate how a magnetic field affects the dynamic behavior of a hybrid nanofluid flow over a curved stretching surface. The unique thermal and rheological characteristics of hybrid nanofluids, which are created by dispersing nanoparticles and micro-sized particles in a base fluid, make them an attractive option for accelerating...
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In the present work, the optical soliton solutions to the 2-dimensional fractional coupled nonlinear Schrödinger model with \(\mathfrak {B}\)eta fractional derivative are found using the unified Riccati equation expansion (\(\textrm{UREE}\)) approach. These solutions are essential to understand wave propagation in a range of physical domains. In re...
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This research delves into a comprehensive exploration of exact solutions for the time-space fractional phi-four equation through the implementation of both the unified method and the modified Khater method. The Phi-four equation, rooted in the Klein-Gordon model, holds significance in diverse scientific realms, such as biological and nuclear physic...
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The stochastic nonlinear Schrödinger model (SNLSM) in (1+1)-dimension with random potential is examined in this paper. The analysis of the evolution of nonlinear dispersive waves in a totally disordered medium depends heavily on the model under investigation. This study has three main objectives. Firstly, for the SNLSM, derive stochastic precise so...
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The article is focused on the analysis of a mathematical model known as the Nizhnik–Novikov–Veselov (SNNV) system, which incorporates a specialized mathematical tool called the truncated M-fractional derivative (TMD). This model has broad applications in various scientific fields and considered an isotropic Lax extension of the one-dimensional Kdv...
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In this study, the modified exponential approach is used to investigate the fractional order longitudinal wave equation in a magneto-elastic circular rod, which represents the nonlinear interplay between dispersion and longitudinal wave velocity depending on the rod’s material and geometry. The time-fractional order is used in the standpoint of con...
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In this paper, we explore applications of the third-order nonlinear Schrödinger’s equation (NLSE) using the rational exp(\(-\varphi \)(\(\zeta \)))-expansion method (REEM) and the modified exponential function method (MEFM), offering insights into wave propagation and soliton behavior in optical communications, nonlinear optics, plasma physics, qua...
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For the sake of intellectual curiosity, in this manuscript we analyse the soliton solutions of a dynamical model namely, the (2+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{d...
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In this paper, we will use the exp(-Φ(η))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(-\Phi (\eta ))$$\end{document}-expansion method to obtain the solitonic wave s...
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Numerous variations of cognitive challenges, such as those in fluid mechanics, plasma physics and nonlinear optics as well as in engineering and mathematics, involve nonlinear partial differential equations. In this study, we explore the (3+1)-dimensional generalized Yu–Toda–Sasa–Fukuyama (YTSF) equation with application in engineering and physical...
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This study is devoted to investigating the soliton solutions of the (2+1) dimensional truncated M-fractional Heisenberg ferromagnetic spin chain model. The model has applications in modern magnetism theory and it illustrates the feature of magnetism to many insulating crystals as well as interaction spins. By deploying two analytical approaches, th...
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The article focuses on exploring three distinct equations: the Jimbo-Miwa equation (JME), the generalized shallow water equation (GSWE), and the Hirota-Satsuma-Ito equation (HSIE). By applying the \(\exp (-\Phi (\eta ))\)-expansion method (EEM), we have successfully obtained novel solutions with trigonometric, elliptic, and hyperbolic properties. T...
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In this article, we examine the Kuramoto–Sivashinsky equation, a nonlinear model that modifies a variety of physical and chemical scenarios. The main goal of this article is to find the analytical solution to the fuzzy fractional Kuramoto–Sivashinsky equations (FFKSEs). We employ the fractional reduced differential transform method (FRDTM) for deal...
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This study uses the Maxwell nanofluid framework to introduce a novel method for simulating blood flow in a stenotic artery. The hyperbolic tangent sigmoid function is incorporated into the suggested model to describe the intricate rheological behavior of the blood-nanoparticle solution. The model offers insights into the flow characteristics and he...
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This paper reveals soliton solutions to (4+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4+1$$\end{document})-dimensional Fokas equation, which is an integrable exte...
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In this research, we address the problem of solving (1 + 1)-dimensional fractional coupled nonlinear Schrödinger equations (FCNLSE) with beta derivatives, which are essential for understanding wave dynamics in various physical systems. These equations have significant importance in practical applications, particularly in the design of optical fiber...
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In this paper, we investigate the impact of the integrability criterion on mixed-derivative nonlinear Schrödinger equations, specifically focusing on the Rangwala-Rao \((\mathcal {R}\mathcal {R})\) equation introduced by A. Rangwala in 1990. Our objective is to enhance our understanding of the dispersion effect by examining innovative soliton wave...
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The unified technique is a direct method that is employed in this study to extract a wide range of accurate solutions of the (2+1)-dimensional Hirota model. The governing model is frequently used in plasma physics to indicate the communications of evolving waves, to simulate the propagation of femtosecond and in nonlinear optical fiber. The main go...
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The fractional coupled Konno-Onno model, which is frequently used in numerous fields of scientific and engineering disciplines, is being investigated in the current study in order to gain an understanding of complex phenomena and systems. The two main goals of this study are to be accomplished. Firstly, the research aims to identify novel solitons...
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Many mathematicians and physicists are interested in Bogoyavlensky–Konopelchenko type equations to illustrate the various dynamics of nonlinear wave phenomena in the fields of fluid mechanics, hydrodynamics, and marine engineering. In this article, we investigate a new generalized (2+1)-dimensional Bogoyavlensky–Konopelchenko (gBK) equation analyti...
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In this paper, we examine the convergence analysis of a variant of Tseng's splitting method for monotone inclusion problem and fixed point problem associated with an infinite family of $ \eta $-demimetric mappings in Hilbert spaces. The qualitative results of the proposed variant shows strong convergence characteristics under a suitable set of cont...
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The fractional coupled nonlinear Schrödinger model (FCNLSM) is widely utilized in various fields such as nonlinear optics, optical communication systems, plasmas and mathematical physics. In this study, we aim to achieve three primary objectives. Firstly, we seek to obtain novel soliton solutions for the FCNLSM, which have not been previously repor...
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In this research, we study traveling wave solutions to the fractional extended nonlinear SchrÖdinger equation (NLSE), and the effects of the third-order dispersion parameter. This equation is used to simulate the propagation of femtosecond, plasma physic and in nonlinear optical fiber. To accomplish this goal, we use the extended simple equation ap...
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This article negotiates the investigation of optical stochastic solitons and other exact stochastic solutions with the fractional stochastic Biswas–Arshed equation (FSBAE) describing the multiplicative white noise of optical signal propagation in birefringent fibers using the modified F-expansion method and Hirota Bilinear method. In order to manag...
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In this study, we investigate the fractional coupled nonlinear Schrödinger equation (FCNLSE) of Manakov type, which has numerous applications in different fields of physics, such as optics and plasma physics. In this study, we employ two different analytical methods, namely the auxiliary equation method (AEM) and the improved F-expansion method, to...
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The aim of this article is to investigate the time fractional coupled nonlinear Schrödinger equation (TFCNLSE) which can be used to describe the interaction among the modes in nonlinear optics and Bose–Einstein condensation. The TFCNLS equation plays a crucial role in soliton wavelength division multiplexing and pulse propagation through a two-mode...
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This study investigates the fractionally coupled nonlinear Schrödinger model (FCNLSM), which has numerous applications in different fields of physics, such as optics, condensed matter physics and plasma physics. The study employs two versatile techniques, the unified technique and the modified F\documentclass[12pt]{minimal} \usepackage{amsmath} \us...
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In this work, we used the space-time fractional coupled Boussinesq (STFCB) model that is essential tools in the study of quantum optics, steady physics, the variational string's acoustic waves, ion vibrational frequencies, hydro-magnetic waves in cold plasma and many other fields.~In order to put such new precise solutions of the aforementioned mod...
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The current research analyses several new optical solitons solutions to the Lakshmanan–Porsezian–Daniel (LPD) equation with the Kerr law of nonlinearity which arises from the application of the Heisenberg spin chain and fiber optics, via two modified analytical methodologies. The auxiliary equation method (AE) and improved F-expansion method are us...
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In this article, we investigate the generalised version of the nonlinear Schrödinger equation namely the fractional Schrödinger–Hirota (NLFSH) equation with third order dispersion and Kerr law of nonlinearity, which describes the dynamics of optical solitons in a dispersive optical fiber. An amelioration of the approaches, namely the improved F-exp...
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The concern of this study is to investigate the optical solitons pluses. The (2+1)-dimensional Kundu–Mukherjee–Naskar (KMN) mathematical model in birefringent fibers is taken under consideration for this sake because this model has great importance in optics and delineate the propagation of soliton dynamics in optical fiber communication system and...
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The main focus of this study is to extract the optical solitons of the two variants of the nonlinear Schrödinger model including the dispersive cubic-quintic nonlinear Schrödinger equation and nonlinear Schrödinger equation with group velocity dispersion. These models have dynamic applications in diversified domains of applied sciences, optical eng...
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In this paper, we examine the solitary wave solutions of the generalised (2 + 1) extended Kadomtsev–Petviashvili (eKP) equation, which is used as model for the surface waves and internal waves in straits or channels and describes the dynamics of nonlinear waves in plasma physics and fluid dynamics. We secure distinct soliton solutions by employing...
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The perturbed nonlinear Schrödinger equation is used frequently to simulate ultra-short pulse lasers, nonlinear optics, optical communication systems, plasmas and other areas of mathematical physics and engineering. The main objective of this study is two fold. (1) to obtain the different kinds of soliton solutions of perturbed nonlinear Schrödinge...
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In this paper, we used the modified \(\frac{G^{'}}{G^{2}}\)-expansion method and unified method to examine the novel complex solutions to the malaria model utilising the conformable derivative, which is an important biological concept. For the with-host malaria model, it is utilised to simulate the dynamics of malaria infection. To assess the effic...
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The fundamental objective of this paper is to tackle the time-fractional order transportation equations through two analytical methods, the method of q-homotopy analysis (q-HAM) and the method of reduced differential transform (RDTM) through numerical computation and simulations. The fractional derivative is considered in Caputo's sense. Three exam...
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In this study, the nonlinear perturbed Schrödinger equation(NPSE) with nonlinear terms as quadratic-cubic law nonlinearity media with the beta derivative is investigated and this investigated model is considered an icon in the field of optical fibers where it describes the wave function or state function of the optical system. Numerous solutions ar...
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In science and technology, the phenomena of transportation are crucial. Advection and diffusion can occur in a wide range of applications. Distinct types of decay rates are feasible for different non-equilibrium systems over lengthy periods of time when it comes to diffusion. In engineering, biology, and ecology, the problems under study are used t...
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In an elastic rod the longitudinal deformation wave propagation is modeled by the nonlinear partial differential equation known as the Pochhammer-Chree equation. In this article, a conformable fractional order generalized Pochhammer-Chree equation with the n order term is studied for constructing some new analytical solutions by using a proficient...
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This paper reveals optical soliton solutions to fiber Bragg gratings (FBGs) with dispersive reflectivity having Kerr law of nonlinear refractive index. Bragg gratings are no doubt a technological spectacle that sustained balance between dispersion and the nonlinear effects that leads to a stable transmission of solitons across intercontinental dist...