Solitary wave solutions of the conformable space–time fractional coupled diffusion equation
In the realm of spatio-temporal fractional dynamics in a predator–prey system, we investigate fractional solitary wave-like solutions using the conformable space–time fractional coupled diffusion equation. To achieve this goal, we utilize the fractional derivative wave transformation approach to con...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124000160 |
| _version_ | 1827316933156929536 |
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| author | K. Manikandan N. Serikbayev D. Aravinthan K. Hosseini |
| author_facet | K. Manikandan N. Serikbayev D. Aravinthan K. Hosseini |
| author_sort | K. Manikandan |
| collection | DOAJ |
| description | In the realm of spatio-temporal fractional dynamics in a predator–prey system, we investigate fractional solitary wave-like solutions using the conformable space–time fractional coupled diffusion equation. To achieve this goal, we utilize the fractional derivative wave transformation approach to convert the conformable space–time fractional coupled nonlinear partial differential equations into equivalent ordinary differential equations. Subsequently, employing the G′G expansion technique, we obtain exact solutions for the transformed coupled ordinary differential equations. With the aid of these solutions and the fractional wave transformation, we construct three distinct fractional solitary wave-like solutions, namely kink-type, periodic, and rational for the considered fractional diffusive predator–prey model. Furthermore, we explore the dynamic attributes of prey and predator population densities by manipulating the space and time fractional-order parameters. Our findings reveal a significant insight: an increase in the fractional order can lead to system stabilization and foster the coexistence of both prey and predator species. |
| first_indexed | 2024-03-08T09:28:01Z |
| format | Article |
| id | doaj.art-955a1dde5719470f9b00bb5d9d7923c3 |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-04-24T23:23:59Z |
| publishDate | 2024-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-955a1dde5719470f9b00bb5d9d7923c32024-03-16T05:09:33ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-03-019100630Solitary wave solutions of the conformable space–time fractional coupled diffusion equationK. Manikandan0N. Serikbayev1D. Aravinthan2K. Hosseini3Center for Computational Modeling, Chennai Institute of Technology, Chennai 600 069, Tamilnadu, India; Corresponding author.Department of General and Theoretical Physics, L. N. Gumilyov Eurasian National University, Astana, 010008, KazakhstanCenter for Computational Modeling, Chennai Institute of Technology, Chennai 600 069, Tamilnadu, IndiaDepartment of Mathematics, Near East University TRNC, Mersin 10, Nicosia 99138, Turkey; Department of Computer Science and Mathematics, Lebanese American University, Beirut, LebanonIn the realm of spatio-temporal fractional dynamics in a predator–prey system, we investigate fractional solitary wave-like solutions using the conformable space–time fractional coupled diffusion equation. To achieve this goal, we utilize the fractional derivative wave transformation approach to convert the conformable space–time fractional coupled nonlinear partial differential equations into equivalent ordinary differential equations. Subsequently, employing the G′G expansion technique, we obtain exact solutions for the transformed coupled ordinary differential equations. With the aid of these solutions and the fractional wave transformation, we construct three distinct fractional solitary wave-like solutions, namely kink-type, periodic, and rational for the considered fractional diffusive predator–prey model. Furthermore, we explore the dynamic attributes of prey and predator population densities by manipulating the space and time fractional-order parameters. Our findings reveal a significant insight: an increase in the fractional order can lead to system stabilization and foster the coexistence of both prey and predator species.http://www.sciencedirect.com/science/article/pii/S2666818124000160Conformable fractional derivativesReaction–diffusion equationsPredator–prey system-expansion methodWave transformation |
| spellingShingle | K. Manikandan N. Serikbayev D. Aravinthan K. Hosseini Solitary wave solutions of the conformable space–time fractional coupled diffusion equation Partial Differential Equations in Applied Mathematics Conformable fractional derivatives Reaction–diffusion equations Predator–prey system -expansion method Wave transformation |
| title | Solitary wave solutions of the conformable space–time fractional coupled diffusion equation |
| title_full | Solitary wave solutions of the conformable space–time fractional coupled diffusion equation |
| title_fullStr | Solitary wave solutions of the conformable space–time fractional coupled diffusion equation |
| title_full_unstemmed | Solitary wave solutions of the conformable space–time fractional coupled diffusion equation |
| title_short | Solitary wave solutions of the conformable space–time fractional coupled diffusion equation |
| title_sort | solitary wave solutions of the conformable space time fractional coupled diffusion equation |
| topic | Conformable fractional derivatives Reaction–diffusion equations Predator–prey system -expansion method Wave transformation |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124000160 |
| work_keys_str_mv | AT kmanikandan solitarywavesolutionsoftheconformablespacetimefractionalcoupleddiffusionequation AT nserikbayev solitarywavesolutionsoftheconformablespacetimefractionalcoupleddiffusionequation AT daravinthan solitarywavesolutionsoftheconformablespacetimefractionalcoupleddiffusionequation AT khosseini solitarywavesolutionsoftheconformablespacetimefractionalcoupleddiffusionequation |