New Solitary Wave Solutions of the Lakshamanan–Porsezian–Daniel Model with the Application of the Φ<sup>6</sup> Method in Fractional Sense
This paper explores a significant fractional model, which is the fractional Lakshamanan–Porsezian–Daniel (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">FLPD</mi></se...
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| Format: | Article |
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MDPI AG
2024-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/1/10 |
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| author | Hicham Saber Hussien Albala Khaled Aldwoah Amer Alsulami Khidir Shaib Mohamed Mohammed Hassan Abdelkader Moumen |
| author_facet | Hicham Saber Hussien Albala Khaled Aldwoah Amer Alsulami Khidir Shaib Mohamed Mohammed Hassan Abdelkader Moumen |
| author_sort | Hicham Saber |
| collection | DOAJ |
| description | This paper explores a significant fractional model, which is the fractional Lakshamanan–Porsezian–Daniel (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">FLPD</mi></semantics></math></inline-formula>) model, widely used in various fields like nonlinear optics and plasma physics. An advanced analytical solution for it is attained by the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="sans-serif">Φ</mi><mn>6</mn></msup></semantics></math></inline-formula> technique. According to this methodology, effective and accurate solutions for wave structures within various types can be produced in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">FLPD</mi></semantics></math></inline-formula> model framework. Solutions such as dark, bright, singular, periodic, and plane waves are studied in detail to identify their stability and behavior. Validations are also brought forward to assess the precision and flexibility of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="sans-serif">Φ</mi><mn>6</mn></msup></semantics></math></inline-formula> technique in modeling fractional models. Therefore, it is established in this study that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="sans-serif">Φ</mi><mn>6</mn></msup></semantics></math></inline-formula> technique represents a powerful tool for examining wave patterns in differential fractional order models. |
| format | Article |
| id | doaj-art-be1e6bf667eb47188650e0b6d43feaaa |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-be1e6bf667eb47188650e0b6d43feaaa2025-01-24T13:33:21ZengMDPI AGFractal and Fractional2504-31102024-12-01911010.3390/fractalfract9010010New Solitary Wave Solutions of the Lakshamanan–Porsezian–Daniel Model with the Application of the Φ<sup>6</sup> Method in Fractional SenseHicham Saber0Hussien Albala1Khaled Aldwoah2Amer Alsulami3Khidir Shaib Mohamed4Mohammed Hassan5Abdelkader Moumen6Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi ArabiaTechnical and Engineering Unit, Applied College (Tanomah), King Khalid University, Abha 61413, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi ArabiaDepartment of Mathematics, Turabah University College, Taif University, Taif 21944, Saudi ArabiaDepartment of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi ArabiaThis paper explores a significant fractional model, which is the fractional Lakshamanan–Porsezian–Daniel (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">FLPD</mi></semantics></math></inline-formula>) model, widely used in various fields like nonlinear optics and plasma physics. An advanced analytical solution for it is attained by the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="sans-serif">Φ</mi><mn>6</mn></msup></semantics></math></inline-formula> technique. According to this methodology, effective and accurate solutions for wave structures within various types can be produced in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">FLPD</mi></semantics></math></inline-formula> model framework. Solutions such as dark, bright, singular, periodic, and plane waves are studied in detail to identify their stability and behavior. Validations are also brought forward to assess the precision and flexibility of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="sans-serif">Φ</mi><mn>6</mn></msup></semantics></math></inline-formula> technique in modeling fractional models. Therefore, it is established in this study that the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="sans-serif">Φ</mi><mn>6</mn></msup></semantics></math></inline-formula> technique represents a powerful tool for examining wave patterns in differential fractional order models.https://www.mdpi.com/2504-3110/9/1/10factional Lakshamanan–Porsezian–Daniel modelconformable derivativeΦ<sup>6</sup> techniquesoliton solutionsstability analysis |
| spellingShingle | Hicham Saber Hussien Albala Khaled Aldwoah Amer Alsulami Khidir Shaib Mohamed Mohammed Hassan Abdelkader Moumen New Solitary Wave Solutions of the Lakshamanan–Porsezian–Daniel Model with the Application of the Φ<sup>6</sup> Method in Fractional Sense Fractal and Fractional factional Lakshamanan–Porsezian–Daniel model conformable derivative Φ<sup>6</sup> technique soliton solutions stability analysis |
| title | New Solitary Wave Solutions of the Lakshamanan–Porsezian–Daniel Model with the Application of the Φ<sup>6</sup> Method in Fractional Sense |
| title_full | New Solitary Wave Solutions of the Lakshamanan–Porsezian–Daniel Model with the Application of the Φ<sup>6</sup> Method in Fractional Sense |
| title_fullStr | New Solitary Wave Solutions of the Lakshamanan–Porsezian–Daniel Model with the Application of the Φ<sup>6</sup> Method in Fractional Sense |
| title_full_unstemmed | New Solitary Wave Solutions of the Lakshamanan–Porsezian–Daniel Model with the Application of the Φ<sup>6</sup> Method in Fractional Sense |
| title_short | New Solitary Wave Solutions of the Lakshamanan–Porsezian–Daniel Model with the Application of the Φ<sup>6</sup> Method in Fractional Sense |
| title_sort | new solitary wave solutions of the lakshamanan porsezian daniel model with the application of the φ sup 6 sup method in fractional sense |
| topic | factional Lakshamanan–Porsezian–Daniel model conformable derivative Φ<sup>6</sup> technique soliton solutions stability analysis |
| url | https://www.mdpi.com/2504-3110/9/1/10 |
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