Yazar "Mahmoud, Mona" seçeneğine göre listele

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    New Numerical Approach of Solving Highly Nonlinear Fractional Partial Differential Equations via Fractional Novel Analytical Method
    (Mdpi, 2022) Sultana, Mariam; Arshad, Uroosa; Abdel-Aty, Abdel-Haleem; Akgul, Ali; Mahmoud, Mona; Eleuch, Hichem
    In this work, the fractional novel analytic method (FNAM) is successfully implemented on some well-known, strongly nonlinear fractional partial differential equations (NFPDEs), and the results show the approach's efficiency. The main purpose is to show the method's strength on FPDEs by minimizing the calculation effort. The novel numerical approach has shown to be the simplest technique for obtaining the numerical solution to any form of the fractional partial differential equation (FPDE).
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    Soliton solutions for the (4
    (Elsevier, 2024) Ashraf, Romana; Amanat, Faiza; Ashraf, Farah; Owyed, Saud; Matoog, R. T.; Mahmoud, Mona; Akgul, Ali
    In this article, we determine various analytical solutions for the (4 + 1)-dimensional Fokas equation, a significant model in mathematical physics with numerous applications in nonlinear dynamics. Utilizing multiple integration techniques such as the improved F-expansion technique and the Jacobi elliptic function method, we retrieve an array of solution types, including traveling waves, periodic solutions, bell-shaped waves, rational functions, and both kink and anti-kink structures. We further explore the complex nature of these solutions through their graphical representations. By applying Maple, we visualize our results in threedimensional (3D), and two-dimensional (2D) formats to illustrate the dynamic behavior of these solutions across various parameters and initial conditions. Our findings provide deeper insights into the properties of the Fokas equation and offer a valuable reference for further studies in nonlinear wave phenomena.
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    Some new soliton solutions to the (3
    (Elsevier, 2023) Ashraf, Romana; Ashraf, Farrah; Akguel, Ali; Ashraf, Saher; Alshahrani, B.; Mahmoud, Mona; Weera, Wajaree
    In this article, The (3 + 1)-dimensional generalized Korteweg-de-Vries-Zakharov-Kuz netsov equation (gKdV-ZKe) which explains the influence of the magnetic field on the weak non-linear ion-acoustic waves investigated in the field of plasma conjured up including both cold and hot electrons. GKdV-zk techniques solutions are obtained using the improved modified extended tanh expansion method, which is one of the most efficient algebraic methods for obtaining accurate solu-tion to nonlinear partial differential equations. We aim to show how the analyzed model's param-eter impact soliton behavior by choosing different bright and single soliton forms and by developing various analytical optical soliton solutions for the explored equation.Methodology: In order to apply the suggested method, we used a complex wave transform to derive the nonlinear ordinary differential form of the analyzed equation. Then, using the method, we were able to obtain the polynomial form, leading to a set of linear equations. The conclusion of solving the linear equations problem, the outcomes of the analyzed model, and the suggested strat-egy are all included in different solution sets. After choosing the appropriate set from these sets, using the solution functions, and utilizing the wave transformation provided by the approach, we were able to arrive at the optical soliton solutions by providing the central equation.Finding: The proposed method has successfully produced a number of soliton solutions and sev-eral analytical optical solutions to such model. The research shows that the parameters of the model may have a variety of effects on the behavior of solitons, categories based on the soliton type. The findings we get in this article can be used to research and compare numerical and experimental data with analytical solving problems in plasma physics.Originality: This study differs from others in that it assessed the impact that parameters of the model have on the actions of solitons, despite the fact that the proposed technique was applied for the first time on the topic under investigation and numerous soliton types were created. This study focuses on the influence of model parameters on solitons behavior.(c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).