Exploring the dynamics of fractional-order nonlinear dispersive wave system through homotopy technique
In this article, we study the time-dependent two-dimensional system of Wu–Zhang equations of fractional order in terms of the Caputo operator, which describes long dispersive waves that minimize and analyze the damaging effects caused by these waves. This article centers on finding soliton solutions...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-04-01
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| Series: | Open Physics |
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| Online Access: | https://doi.org/10.1515/phys-2025-0128 |
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| author | Kumar Chiranahalli Vijaya Darshan Prakasha Doddabhadrappla Gowda Turki Nasser Bin |
| author_facet | Kumar Chiranahalli Vijaya Darshan Prakasha Doddabhadrappla Gowda Turki Nasser Bin |
| author_sort | Kumar Chiranahalli Vijaya Darshan |
| collection | DOAJ |
| description | In this article, we study the time-dependent two-dimensional system of Wu–Zhang equations of fractional order in terms of the Caputo operator, which describes long dispersive waves that minimize and analyze the damaging effects caused by these waves. This article centers on finding soliton solutions of a non-linear (2+12+1)-dimensional time-fractional Wu–Zhang system, which has become a significant point of interest for its ability to describe the dynamics of long dispersive gravity water waves. The semi-analytical method called the qq-homotopy analysis method in amalgamation with the Laplace transform is applied to uncover an analytical solution for this system of equations. The outcomes obtained through the considered method are in the form of a series solution, and they converge swiftly. The results coincide with the exact solution are portrayed through graphs and carried out numerical simulations which shows minimum residual error. This analysis shows that the technique used here is a reliable and well organized, which enhances in analyzing the higher-dimensional non-linear fractional differential equations in various sectors of science and engineering. |
| format | Article |
| id | doaj-art-6aa12677ba10477f830c191efa3b03ed |
| institution | Kabale University |
| issn | 2391-5471 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Physics |
| spelling | doaj-art-6aa12677ba10477f830c191efa3b03ed2025-08-20T03:53:42ZengDe GruyterOpen Physics2391-54712025-04-01231758910.1515/phys-2025-0128Exploring the dynamics of fractional-order nonlinear dispersive wave system through homotopy techniqueKumar Chiranahalli Vijaya Darshan0Prakasha Doddabhadrappla Gowda1Turki Nasser Bin2Department of Mathematics, Davangere University, Shivagangotri, Davangere - 577007, IndiaDepartment of Mathematics, Davangere University, Shivagangotri, Davangere - 577007, IndiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box - 2455, Riyadh - 11451, Saudi ArabiaIn this article, we study the time-dependent two-dimensional system of Wu–Zhang equations of fractional order in terms of the Caputo operator, which describes long dispersive waves that minimize and analyze the damaging effects caused by these waves. This article centers on finding soliton solutions of a non-linear (2+12+1)-dimensional time-fractional Wu–Zhang system, which has become a significant point of interest for its ability to describe the dynamics of long dispersive gravity water waves. The semi-analytical method called the qq-homotopy analysis method in amalgamation with the Laplace transform is applied to uncover an analytical solution for this system of equations. The outcomes obtained through the considered method are in the form of a series solution, and they converge swiftly. The results coincide with the exact solution are portrayed through graphs and carried out numerical simulations which shows minimum residual error. This analysis shows that the technique used here is a reliable and well organized, which enhances in analyzing the higher-dimensional non-linear fractional differential equations in various sectors of science and engineering.https://doi.org/10.1515/phys-2025-0128fractional wu–zhang equationq-homotopy analysis transform methodcaputo-fractional operatorlaplace transform |
| spellingShingle | Kumar Chiranahalli Vijaya Darshan Prakasha Doddabhadrappla Gowda Turki Nasser Bin Exploring the dynamics of fractional-order nonlinear dispersive wave system through homotopy technique Open Physics fractional wu–zhang equation q-homotopy analysis transform method caputo-fractional operator laplace transform |
| title | Exploring the dynamics of fractional-order nonlinear dispersive wave system through homotopy technique |
| title_full | Exploring the dynamics of fractional-order nonlinear dispersive wave system through homotopy technique |
| title_fullStr | Exploring the dynamics of fractional-order nonlinear dispersive wave system through homotopy technique |
| title_full_unstemmed | Exploring the dynamics of fractional-order nonlinear dispersive wave system through homotopy technique |
| title_short | Exploring the dynamics of fractional-order nonlinear dispersive wave system through homotopy technique |
| title_sort | exploring the dynamics of fractional order nonlinear dispersive wave system through homotopy technique |
| topic | fractional wu–zhang equation q-homotopy analysis transform method caputo-fractional operator laplace transform |
| url | https://doi.org/10.1515/phys-2025-0128 |
| work_keys_str_mv | AT kumarchiranahallivijayadarshan exploringthedynamicsoffractionalordernonlineardispersivewavesystemthroughhomotopytechnique AT prakashadoddabhadrapplagowda exploringthedynamicsoffractionalordernonlineardispersivewavesystemthroughhomotopytechnique AT turkinasserbin exploringthedynamicsoffractionalordernonlineardispersivewavesystemthroughhomotopytechnique |