Browsing by Author "Fayz-Al-Asad, Md."

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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, 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.