Computational and numerical simulations of nonlinear fractional Ostrovsky equation
This article investigates the accuracy of the obtained analytical solutions of the nonlinear fractional Ostrovsky (NLFO.) equation. The researched solutions are obtained by exploiting the well-known generalized Tanh–function (GTF.) method with the Atengana– conformable fractional (ACF.) derivative i...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2022-09-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016821008425 |
| _version_ | 1811275128300896256 |
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| author | Mohamed Omri Abdel-Haleem Abdel-Aty S. Abdel-Khalek E.M. Khalil Mostafa M.A. Khater |
| author_facet | Mohamed Omri Abdel-Haleem Abdel-Aty S. Abdel-Khalek E.M. Khalil Mostafa M.A. Khater |
| author_sort | Mohamed Omri |
| collection | DOAJ |
| description | This article investigates the accuracy of the obtained analytical solutions of the nonlinear fractional Ostrovsky (NLFO.) equation. The researched solutions are obtained by exploiting the well-known generalized Tanh–function (GTF.) method with the Atengana– conformable fractional (ACF.) derivative in the wave transformation. Five–numerical schemes (Adomian decomposition (AD), El Kalla (EK), cubic B-Spline (CBS), extended cubic B-Spline (ECBS), and exponential cubic B-Spline (ExCBS)) handle these solutions to check their solutions. The investigated fractional model is a general form of the KdV equation; however, the KdV equation’s solutions replace this effect with radiating inertia gravity waves. This model also describes a weak description of nonlinear ocean wave processes considering Earth rotation. The obtained analytical and numerical results are sketched through Mathematica 12 in different plot types to explain the waves’ dynamical behavior. Additionally, the computational obtained solutions’ stability is investigated. Finally, the paper’s contribution and obtained results’ novelty are demonstrated by comparing our solutions with those that have been obtained in previous scientific articles. |
| first_indexed | 2024-04-12T23:32:35Z |
| format | Article |
| id | doaj.art-4c467b18129241939f3ff06d74321de4 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-12T23:32:35Z |
| publishDate | 2022-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-4c467b18129241939f3ff06d74321de42022-12-22T03:12:15ZengElsevierAlexandria Engineering Journal1110-01682022-09-0161968876895Computational and numerical simulations of nonlinear fractional Ostrovsky equationMohamed Omri0Abdel-Haleem Abdel-Aty1S. Abdel-Khalek2E.M. Khalil3Mostafa M.A. Khater4Deanship of Scientific Research, King Abdulaziz University, Jeddah, Saudi ArabiaDepartment of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia; Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, EgyptDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia; Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, EgyptDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia; Mathematics Department, Faculty of Science, Al-Azher University, Nassr City, Cairo 11884, EgyptDepartment of Mathematics, Faculty of Science, Jiangsu University, 212013 Zhenjiang, China; Department of Basic Science, Obour High Institute for Engineering and Technology, 11828 Cairo, Egypt; Corresponding author at: Department of Mathematics, Faculty of Science, Jiangsu University, 212013 Zhenjiang, China.This article investigates the accuracy of the obtained analytical solutions of the nonlinear fractional Ostrovsky (NLFO.) equation. The researched solutions are obtained by exploiting the well-known generalized Tanh–function (GTF.) method with the Atengana– conformable fractional (ACF.) derivative in the wave transformation. Five–numerical schemes (Adomian decomposition (AD), El Kalla (EK), cubic B-Spline (CBS), extended cubic B-Spline (ECBS), and exponential cubic B-Spline (ExCBS)) handle these solutions to check their solutions. The investigated fractional model is a general form of the KdV equation; however, the KdV equation’s solutions replace this effect with radiating inertia gravity waves. This model also describes a weak description of nonlinear ocean wave processes considering Earth rotation. The obtained analytical and numerical results are sketched through Mathematica 12 in different plot types to explain the waves’ dynamical behavior. Additionally, the computational obtained solutions’ stability is investigated. Finally, the paper’s contribution and obtained results’ novelty are demonstrated by comparing our solutions with those that have been obtained in previous scientific articles.http://www.sciencedirect.com/science/article/pii/S111001682100842504.20.Jb05.45.Yv42.65.Tg |
| spellingShingle | Mohamed Omri Abdel-Haleem Abdel-Aty S. Abdel-Khalek E.M. Khalil Mostafa M.A. Khater Computational and numerical simulations of nonlinear fractional Ostrovsky equation Alexandria Engineering Journal 04.20.Jb 05.45.Yv 42.65.Tg |
| title | Computational and numerical simulations of nonlinear fractional Ostrovsky equation |
| title_full | Computational and numerical simulations of nonlinear fractional Ostrovsky equation |
| title_fullStr | Computational and numerical simulations of nonlinear fractional Ostrovsky equation |
| title_full_unstemmed | Computational and numerical simulations of nonlinear fractional Ostrovsky equation |
| title_short | Computational and numerical simulations of nonlinear fractional Ostrovsky equation |
| title_sort | computational and numerical simulations of nonlinear fractional ostrovsky equation |
| topic | 04.20.Jb 05.45.Yv 42.65.Tg |
| url | http://www.sciencedirect.com/science/article/pii/S1110016821008425 |
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