Browsing by Author "Akbar, M.A."

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    A comprehensive study on geometric shape optical soliton solutions to the time-factional nonlinear Schrödinger-Hirota equation
    (Elsevier B.V., 2024-09-12) Khatun, M.M.; Khan, S.; Akbar, M.A.
    In this study, we investigate the analytical soliton solutions of a fundamental model, namely the nonlinear Schrödinger-Hirota equation, in the context of beta time-fractional derivative. We adopt the (ω′/ω, 1/ω)-expansion method, which is a reliable and straightforward approach to extract fresh and general soliton solutions in terms of hyperbolic, trigonometric, and rational functions. The solitons include anti-kink, anti-bell-shaped, bell-shaped, and periodic solitons. These solitons have significant applications in various scientific fields, such as optical fiber communications, signal processing, plasma physics, and trans-oceanic data transfer. This study demonstrates the significance of fractional-order differentiation in revealing new solitons. We also provide a comprehensive comparison with existing literature in normal and anomalous dispersion regions, highlighting the uniqueness of the solutions. Moreover, the graphical representations are used to illustrate the properties and potential applications of these solitons. This research might contribute to the advancement of nonlinear optical research and technology
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    Numerical and analytical solutions of new Blasius equation for turbulent flow
    (Elsevier Ltd, 2023) Rahman, M.M.,; Khan, S.,; Akbar, M.A.
    The Blasius equation for laminar flow comes from the Prandtl boundary layer equations. In this article, we establish a new and generic Blasius equation for turbulent flow derived from the turbulent boundary layer equation that can be used for turbulent as well as laminar flow. The analytical and numerical solutions have been investigated under specific conditions to the developed new Blasius equation. The analytical and numerical results have been compared through tables and graphs to validate the established model. In fluid dynamics, analytical solutions to complicated systems are tedious and time-consuming. Changing one or more constraints can introduce new challenges. In this case, symbolic computation software provides an easier and more flexible solution for fluid dynamical systems, even if boundary conditions are adjusted to explain reality. Therefore, the MATLAB code is used to investigate the new third-order Blasius equation. The comparison and graphical representations demonstrate that the achieved results are encouraging.