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    A Comparative Analysis of the Fractional-Order Coupled Korteweg-De Vries Equations with the Mittag-Leffler Law
    (Hindawi Ltd, 2022) Aljahdaly, Noufe H.; Akgul, Ali; Shah, Rasool; Mahariq, Ibrahim; Kafle, Jeevan
    This article applies efficient methods, namely, modified decomposition method and new iterative transformation method, to analyze a nonlinear system of Korteweg-de Vries equations with the Atangana-Baleanu fractional derivative. The nonlinear fractional coupled systems investigated in this current analysis are the system of Korteweg-de Vries and the modified system of Korteweg-de Vries equations applied as a model in nonlinear physical phenomena arising in chemistry, biology, physics, and applied sciences. Approximate analytical results are represented in the form of a series with straightforward components, and some aspects showed an appropriate dependence on the values of the fractional-order derivatives. The convergence and uniqueness analysis is carried out. To comprehend the analytical procedure of both methods, three test examples are provided for the analytical results of the time-fractional KdV equation. Additionally, the efficiency of the mentioned procedures and the reduction in calculations provide broader applicability. It is also illustrated that the findings of the current methodology are in close harmony with the exact solutions. The series result achieved applying this technique is proved to be accurate and reliable with minimal calculations. The numerical simulations for obtained solutions are discussed for different values of the fractional order.
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    Öğe
    Significance of melting phenomena on Darcy-Forchheimer flow of trihybrid nanofluid over a disk in the presence of thermophoresis particles deposition
    (Springernature, 2025) Mahariq, Ibrahim; Abbas, Munawar; Fatima, Nahid; Akgul, Ali; Faqihi, Abdullah A.
    The purpose of the proposed study is to examine the significance of Marangoni convection and inclined MHD on an axisymmetric Darcy-Forchheimer flow of a ternary hybrid nanofluid across an infinite disk that includes melting processes. The thermophoresis particle deposition, Joule heating, taken into account. This suggested model aims to compare the Yamada-Ota model and Xue thermal conductivity ternary hybrid nanofluid models' performances. In order to claim the assets of the trihybrid nanofluid model, Fe3O4,Cu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F{e}_{3}O}_{4}, Cu$$\end{document} and MoS2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${MoS}_{2}$$\end{document} particles are combined with an improper fluid composed of 50%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$50\%$$\end{document} ethylene glycol and 50%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$50\%$$\end{document} water. The improvement of heat transfer processes in thermal management systems, such as those used in the cooling of electronic devices, automobiles, and aerospace components, depends heavily on this model. It can also be used in energy systems, where it can increase the efficiency of solar collectors, nuclear reactors, and geothermal reservoirs by optimizing heat transport in nanofluids. Designing effective filtration, coating, and drug delivery systems requires an understanding of particle deposition behavior, which is made possible by the use of thermophoresis. By utilizing the proper variables, the system of partial differential equations can be converted into an ordinary differential equation. The bvp4c approach provides a numerical solution to this problem. Graphs and Tables are used to examine the effects of various corporal and flow constraints on thermal, solutal, and velocity distributions, as well as the impact of the heat/mass phenomenon on flow behavior. At higher melting parameter, the temperature and horizontal velocity distribution of the ternary hybrid nanofluid are shown to be predominant. Increases in the rate of heat and mass transmission are correlated with increases in the Marangoni convection parameter.