Application of the New Mapping Method to Complex Three Coupled Maccari’s System Possessing M-Fractional Derivative
In this academic investigation, an innovative mapping approach is applied to complex three coupled Maccari’s system to unveil novel soliton solutions. This is achieved through the utilization of M-Truncated fractional derivative with employing the new mapping method and computer algebraic syatem (CA...
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| Format: | Article |
| Language: | English |
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Akif AKGUL
2024-07-01
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| Series: | Chaos Theory and Applications |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3639839 |
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| author | Jan Martinovic Aziz Ur Rehman Muhammad Bilal Riaz |
| author_facet | Jan Martinovic Aziz Ur Rehman Muhammad Bilal Riaz |
| author_sort | Jan Martinovic |
| collection | DOAJ |
| description | In this academic investigation, an innovative mapping approach is applied to complex three coupled Maccari’s system to unveil novel soliton solutions. This is achieved through the utilization of M-Truncated fractional derivative with employing the new mapping method and computer algebraic syatem (CAS) such as Maple. The derived solutions in the form of hyperbolic and trigonometric functions. Our study elucidates a variety of soliton solutions such as periodic, singular, dark, kink, bright, dark-bright solitons solutions. To facilitate comprehension, with certain solutions being visually depicted through 2-dimensional, contour, 3-dimensional, and phase plots depicting bifurcation characteristics utilizing Maple software. Furthermore, the incorporation of M-Truncated derivative enables a more extensive exploration of solution patterns. Our study establishes a connection between computer science and soliton physics, emphasizing the pivotal role of soliton phenomena in advancing simulations and computational modeling. Analytical solutions are subsequently generated through the application of the new mapping method. Following this, a thorough examination of the dynamic nature of the equation is conducted from various perspectives. In essence, understanding the dynamic characteristics of systems is of great importance for predicting outcomes and advancing new technologies. This research significantly contributes to the convergence of theoretical mathematics and applied computer science, emphasizing the crucial role of solitons in scientific disciplines. |
| format | Article |
| id | doaj-art-2be8df352313497d8d5679b91ed4844a |
| institution | Kabale University |
| issn | 2687-4539 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Akif AKGUL |
| record_format | Article |
| series | Chaos Theory and Applications |
| spelling | doaj-art-2be8df352313497d8d5679b91ed4844a2025-01-23T18:19:34ZengAkif AKGULChaos Theory and Applications2687-45392024-07-016318019110.51537/chaos.14147821971Application of the New Mapping Method to Complex Three Coupled Maccari’s System Possessing M-Fractional DerivativeJan Martinovic0https://orcid.org/0000-0001-7944-8956Aziz Ur Rehman1https://orcid.org/0000-0002-8804-3915Muhammad Bilal Riaz2https://orcid.org/0000-0001-5153-297XVSB-Technical University of OstravaUniversity of Management and TechnologyVSB-Technical University of OstravaIn this academic investigation, an innovative mapping approach is applied to complex three coupled Maccari’s system to unveil novel soliton solutions. This is achieved through the utilization of M-Truncated fractional derivative with employing the new mapping method and computer algebraic syatem (CAS) such as Maple. The derived solutions in the form of hyperbolic and trigonometric functions. Our study elucidates a variety of soliton solutions such as periodic, singular, dark, kink, bright, dark-bright solitons solutions. To facilitate comprehension, with certain solutions being visually depicted through 2-dimensional, contour, 3-dimensional, and phase plots depicting bifurcation characteristics utilizing Maple software. Furthermore, the incorporation of M-Truncated derivative enables a more extensive exploration of solution patterns. Our study establishes a connection between computer science and soliton physics, emphasizing the pivotal role of soliton phenomena in advancing simulations and computational modeling. Analytical solutions are subsequently generated through the application of the new mapping method. Following this, a thorough examination of the dynamic nature of the equation is conducted from various perspectives. In essence, understanding the dynamic characteristics of systems is of great importance for predicting outcomes and advancing new technologies. This research significantly contributes to the convergence of theoretical mathematics and applied computer science, emphasizing the crucial role of solitons in scientific disciplines.https://dergipark.org.tr/en/download/article-file/3639839complex three coupled maccari’s systema new mapping method; soliton patternsbifurcation; m-truncated fractional derivative |
| spellingShingle | Jan Martinovic Aziz Ur Rehman Muhammad Bilal Riaz Application of the New Mapping Method to Complex Three Coupled Maccari’s System Possessing M-Fractional Derivative Chaos Theory and Applications complex three coupled maccari’s system a new mapping method; soliton patterns bifurcation; m-truncated fractional derivative |
| title | Application of the New Mapping Method to Complex Three Coupled Maccari’s System Possessing M-Fractional Derivative |
| title_full | Application of the New Mapping Method to Complex Three Coupled Maccari’s System Possessing M-Fractional Derivative |
| title_fullStr | Application of the New Mapping Method to Complex Three Coupled Maccari’s System Possessing M-Fractional Derivative |
| title_full_unstemmed | Application of the New Mapping Method to Complex Three Coupled Maccari’s System Possessing M-Fractional Derivative |
| title_short | Application of the New Mapping Method to Complex Three Coupled Maccari’s System Possessing M-Fractional Derivative |
| title_sort | application of the new mapping method to complex three coupled maccari s system possessing m fractional derivative |
| topic | complex three coupled maccari’s system a new mapping method; soliton patterns bifurcation; m-truncated fractional derivative |
| url | https://dergipark.org.tr/en/download/article-file/3639839 |
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