Browsing by Author "Alam, Md. Nur"

Now showing 1 - 5 of 5

An Analytical Method for Solving Exact Solutions of the Nonlinear Bogoyavlenskii Equation and the Nonlinear Diffusive Predator-Prey System
(Elsevier Science Bv, 2016) Alam, Md. Nur; Tunc, Cemil
In this article, we apply the exp(-Phi(xi))-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs) via the nonlinear diffusive predator-prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator-prey system and the Bogoyavlenskii equations by the help of programming language Maple. (C) 2016 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
B-Spline Curve Theory: an Overview and Applications in Real Life
(de Gruyter Poland Sp Z O O, 2024) Hasan, Md. Shahid; Alam, Md. Nur; Fayz-Al-Asad, Md.; Muhammad, Noor; Tunc, Cemil
This study commences by delving into B-spline curves, their essential properties, and their practical implementations in the real world. It also examines the role of knot vectors, control points, and de Boor's algorithm in creating an elegant and seamless curve. Beginning with an overview of B-spline curve theory, we delve into the necessary properties that make these curves unique. We explore their local control, smoothness, and versatility, making them well-suited for a wide range of applications. Furthermore, we examine some basic applications of B-spline curves, from designing elegant automotive curves to animating lifelike characters in the entertainment industry, making a significant impact. Utilizing the de Boor algorithm, we intricately shape the contours of everyday essentials by applying a series of control points in combination with a B-spline curve. In addition, we offer valuable insights into the diverse applications of B-spline curves in computer graphics, toy design, the electronics industry, architecture, manufacturing, and various engineering sectors. We highlight their practical utility in manipulating the shape and behavior of the curve, serving as a bridge between theory and application.
Bifurcation Analysis and Solitary Wave Analysis of the Nonlinear Fractional Soliton Neuron Model
(Springer int Publ Ag, 2023) Alam, Md. Nur; Akash, Hemel Sharker; Saha, Uzzal; Hasan, Md. Shahid; Parvin, Mst. Wahida; Tunc, Cemil
Fractional nonlinear soliton neuron model (FNLSNM) equation is mathematical interpretations employed to describe a wide range of complicated phenomena occurring in neuroscience and obscure mode of action of numerous anesthetics. FNLSNM equation explains how action potential is started and performed along axons depending on a thermodynamic theory of nerve pulse propagation. The signals that pass through the cell membrane were suggested to be in different forms of solitary sound pulses which can be modeled as solitons. So, the scientific community has exposed momentous interest in FNLSNM equation and their Bifurcation analysis (BA) and solitary wave analysis (SWA). This study employs the modified (G '/G)-expansion (M-(G '/G)-E) method to derive BA and SWA for the FNLSNM equation, utilizing the Jumarie's fractional derivative (JFD). 3D and BA figures are presented of FNLSNM equation. Furthermore, 2D plots are produced to examine how the fractional parameter (FP) and time space parameter (TSP) affects the SWA. The Hamiltonian function (HF) is established to advance analyses the dynamics of the phase plane (PP). The simulations were performed through Python and MAPLE software instruments. The effects of different studies showed that the M-(G '/G)-E method is pretty well-organized and is well well-matched for the difficulties arising in neuroscience and mathematical physics.
Bifurcation, Phase Plane Analysis and Exact Soliton Solutions in the Nonlinear Schrodinger Equation With Atangana's Conformable Derivative
(Pergamon-elsevier Science Ltd, 2024) Alam, Md. Nur; Iqbal, Mujahid; Hassan, Mohammad; Fayz-Al-Asad, Md.; Hossain, Muhammad Sajjad; Tunc, Cemil
The nonlinear Schrodinger equation (NLSE) with Atangana's conformable fractional derivative (ACFD) is an equation that describes how the quantum state of a physical system changes in time. This present study examines the exact soliton results (ESRs) and analyze their bifurcations and phase plane (PP) of the NLSE with ACFD through the modified (G '/G)-expansion scheme (MG '/GES). Firstly, ACFD and its properties are included and then by MG '/GES, the exact soliton results and analyze their bifurcations and phase plane of NLSE, displayed with the ACFD, are classified. These obtained ESRs include periodic wave pulse, bright-dark periodic wave pulse, multiple bright-dark soliton pulse, and so many types. We provide 2-D, 3-D and contour diagrams, Hamiltonian function (HF) for phase plane dynamics analysis and bifurcation analysis diagrams to examine the nonlinear effects and the impact of fractional and time parameters on these obtained ESRs. The obtained ESRs illustration the novelty and prominence of the dynamical construction and promulgation performance of the resultant equation and also have practical effects for real world problems. The ESRs obtained with MG '/GES show that this scheme is very humble, well-organized and can be implemented to other the NLSE with ACFD.
Dynamics of Damped and Undamped Wave Natures of the Fractional Kraenkel-Manna System in Ferromagnetic Materials
(Shahid Chamran Univ Ahvaz, Iran, 2024) Alam, Md. Nur; Rahim, Md. Abdur; Hossain, Md. Najmul; Tung, Cemil
This research considers the Kraenkel-Manna-Merle system with an M -truncated derivative (K -M -M -S -M -T -D) that defines the magnetic field propagation (M -F -P) in ferromagnetic materials with zero conductivity (F -M -Z -C) and uses the Sardar subequation method (S -S -E -M). Our goal is to acquire soliton solutions (SSs) of K -M -M -S -M -T -D via the S -S -E -M. To our knowledge, no one has considered the SSs to the K-M-M-S-MTD with or without a damping effect (DE) via the S -S -E -M. The SSs are achieved as the M -shape, periodic wave shape, W -shape, kink, anti -parabolic, and singular kink solitons in terms of free parameters. We utilize Maple to expose pictures in three-dimensional (3-D), contour and two-dimensional (2-D) for different values of fractional order (FO) of the got SSs, and we discuss the effect of the FO of the K-M-M-S-MTD via the S -S -E -M, which has not been discussed in the previous literature. All wave phenomena are applied to optical fiber communication, signal transmission, porous mediums, magneto -acoustic waves in plasma, electromagnetism, fluid dynamics, chaotic systems, coastal engineering, and so on. The achieved SSs prove that the S -S -E -M is very simple and effective for nonlinear science and engineering for examining nonlinear fractional differential equations (N -L -F -D -Es).