Solitary Wave Solutions to a Fractional-Order Fokas Equation via the Improved Modified Extended Tanh-Function Approach
This research employs the improved modified extended tanh-function technique to explore several solitary wave solutions to the fractional-order Fokas equation. The propagation of waves in fluid dynamics and optical systems are two examples of various natural phenomena that are effectively addressed...
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| Format: | Article |
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MDPI AG
2024-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/1/109 |
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| author | M. B. Almatrafi |
| author_facet | M. B. Almatrafi |
| author_sort | M. B. Almatrafi |
| collection | DOAJ |
| description | This research employs the improved modified extended tanh-function technique to explore several solitary wave solutions to the fractional-order Fokas equation. The propagation of waves in fluid dynamics and optical systems are two examples of various natural phenomena that are effectively addressed by the fractional-order Fokas equation. The model captures a generalization of the integer derivative form by including fractional derivatives defined in the conformable sense. We use the phase portrait theory to investigate the existence of traveling wave solutions. The improved modified extended tanh-function technique is successfully applied as a reliable analytical procedure to derive several solitary wave solutions, providing an approachable structure to deal with the complexity introduced by the fractional order. The extracted solutions, which are illustrated by hyperbolic, trigonometric, and rational functions, exhibit a variety of solitary wave shapes, such as bell-shaped, kink, and anti-kink patterns. We additionally evaluate how well the employed method performs in comparison to other approaches. Furthermore, some graphical visualizations are provided to clearly demonstrate the physical behavior of the obtained solutions under various parameter values. The outcomes highlight the effectiveness and adaptability of the proposed strategy in resolving fractional nonlinear differential equations and expand our knowledge of fractional-order systems. |
| format | Article |
| id | doaj-art-69580ae9b75448e294fc4063961d4ca6 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-69580ae9b75448e294fc4063961d4ca62025-01-10T13:18:16ZengMDPI AGMathematics2227-73902024-12-0113110910.3390/math13010109Solitary Wave Solutions to a Fractional-Order Fokas Equation via the Improved Modified Extended Tanh-Function ApproachM. B. Almatrafi0Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawara 42353, Saudi ArabiaThis research employs the improved modified extended tanh-function technique to explore several solitary wave solutions to the fractional-order Fokas equation. The propagation of waves in fluid dynamics and optical systems are two examples of various natural phenomena that are effectively addressed by the fractional-order Fokas equation. The model captures a generalization of the integer derivative form by including fractional derivatives defined in the conformable sense. We use the phase portrait theory to investigate the existence of traveling wave solutions. The improved modified extended tanh-function technique is successfully applied as a reliable analytical procedure to derive several solitary wave solutions, providing an approachable structure to deal with the complexity introduced by the fractional order. The extracted solutions, which are illustrated by hyperbolic, trigonometric, and rational functions, exhibit a variety of solitary wave shapes, such as bell-shaped, kink, and anti-kink patterns. We additionally evaluate how well the employed method performs in comparison to other approaches. Furthermore, some graphical visualizations are provided to clearly demonstrate the physical behavior of the obtained solutions under various parameter values. The outcomes highlight the effectiveness and adaptability of the proposed strategy in resolving fractional nonlinear differential equations and expand our knowledge of fractional-order systems.https://www.mdpi.com/2227-7390/13/1/109traveling wavesphase portraitsolitonfractional derivativeequilibrium pointsstability |
| spellingShingle | M. B. Almatrafi Solitary Wave Solutions to a Fractional-Order Fokas Equation via the Improved Modified Extended Tanh-Function Approach Mathematics traveling waves phase portrait soliton fractional derivative equilibrium points stability |
| title | Solitary Wave Solutions to a Fractional-Order Fokas Equation via the Improved Modified Extended Tanh-Function Approach |
| title_full | Solitary Wave Solutions to a Fractional-Order Fokas Equation via the Improved Modified Extended Tanh-Function Approach |
| title_fullStr | Solitary Wave Solutions to a Fractional-Order Fokas Equation via the Improved Modified Extended Tanh-Function Approach |
| title_full_unstemmed | Solitary Wave Solutions to a Fractional-Order Fokas Equation via the Improved Modified Extended Tanh-Function Approach |
| title_short | Solitary Wave Solutions to a Fractional-Order Fokas Equation via the Improved Modified Extended Tanh-Function Approach |
| title_sort | solitary wave solutions to a fractional order fokas equation via the improved modified extended tanh function approach |
| topic | traveling waves phase portrait soliton fractional derivative equilibrium points stability |
| url | https://www.mdpi.com/2227-7390/13/1/109 |
| work_keys_str_mv | AT mbalmatrafi solitarywavesolutionstoafractionalorderfokasequationviatheimprovedmodifiedextendedtanhfunctionapproach |