Dynamics of the Traveling Wave Solutions of Fractional Date–Jimbo–Kashiwara–Miwa Equation via Riccati–Bernoulli Sub-ODE Method through Bäcklund Transformation
The dynamical wave solutions of the time–space fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equation have been obtained in this article using an innovative and efficient technique including the Riccati–Bernoulli sub-ODE method through Bäcklund transformation. Fractional-order derivatives enter into p...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-08-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/8/9/497 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850261379932487680 |
|---|---|
| author | M. Mossa Al-Sawalha Saima Noor Mohammad Alqudah Musaad S. Aldhabani Roman Ullah |
| author_facet | M. Mossa Al-Sawalha Saima Noor Mohammad Alqudah Musaad S. Aldhabani Roman Ullah |
| author_sort | M. Mossa Al-Sawalha |
| collection | DOAJ |
| description | The dynamical wave solutions of the time–space fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equation have been obtained in this article using an innovative and efficient technique including the Riccati–Bernoulli sub-ODE method through Bäcklund transformation. Fractional-order derivatives enter into play for their novel contribution to the enhancement of the characterization of dynamic waves while providing better modeling ability compared to integer types of derivatives. The solutions of the above-mentioned time–space fractional Date–Jimbo–Kashiwara–Miwa equation have tremendous importance in numerous scientific scenarios. The regular dynamical wave solutions of the aforementioned equation encompass three fundamental functions: trigonometric, hyperbolic, and rational functions will be among the topics covered. These solutions are graphically classified into three categories: compacton kink solitary wave solutions, kink soliton wave solutions and anti-kink soliton wave solutions. In addition, to explore the impact of the fractional parameter (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>) on those solutions, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>D</mi></mrow></semantics></math></inline-formula> plots are utilized, while <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mi>D</mi></mrow></semantics></math></inline-formula> plots are applied to present the solutions involving the integer-order derivatives. |
| format | Article |
| id | doaj-art-219f1eb646e247fcaef60eb47b298ff6 |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-219f1eb646e247fcaef60eb47b298ff62025-08-20T01:55:27ZengMDPI AGFractal and Fractional2504-31102024-08-018949710.3390/fractalfract8090497Dynamics of the Traveling Wave Solutions of Fractional Date–Jimbo–Kashiwara–Miwa Equation via Riccati–Bernoulli Sub-ODE Method through Bäcklund TransformationM. Mossa Al-Sawalha0Saima Noor1Mohammad Alqudah2Musaad S. Aldhabani3Roman Ullah4Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi ArabiaDepartment of Basic Sciences, General Administration of Preparatory Year, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi ArabiaDepartment of Basic Sciences, School of Electrical Engineering & Information Technology, German Jordanian University, Amman 11180, JordanDepartment of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaDepartment of General Studies, Higher Colleges of Technology, Dubai Women Campus, Dubai 16062, United Arab EmiratesThe dynamical wave solutions of the time–space fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equation have been obtained in this article using an innovative and efficient technique including the Riccati–Bernoulli sub-ODE method through Bäcklund transformation. Fractional-order derivatives enter into play for their novel contribution to the enhancement of the characterization of dynamic waves while providing better modeling ability compared to integer types of derivatives. The solutions of the above-mentioned time–space fractional Date–Jimbo–Kashiwara–Miwa equation have tremendous importance in numerous scientific scenarios. The regular dynamical wave solutions of the aforementioned equation encompass three fundamental functions: trigonometric, hyperbolic, and rational functions will be among the topics covered. These solutions are graphically classified into three categories: compacton kink solitary wave solutions, kink soliton wave solutions and anti-kink soliton wave solutions. In addition, to explore the impact of the fractional parameter (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>) on those solutions, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>D</mi></mrow></semantics></math></inline-formula> plots are utilized, while <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mi>D</mi></mrow></semantics></math></inline-formula> plots are applied to present the solutions involving the integer-order derivatives.https://www.mdpi.com/2504-3110/8/9/497fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equationBäcklund transformationnonlinear differential equationsexact solutions |
| spellingShingle | M. Mossa Al-Sawalha Saima Noor Mohammad Alqudah Musaad S. Aldhabani Roman Ullah Dynamics of the Traveling Wave Solutions of Fractional Date–Jimbo–Kashiwara–Miwa Equation via Riccati–Bernoulli Sub-ODE Method through Bäcklund Transformation Fractal and Fractional fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equation Bäcklund transformation nonlinear differential equations exact solutions |
| title | Dynamics of the Traveling Wave Solutions of Fractional Date–Jimbo–Kashiwara–Miwa Equation via Riccati–Bernoulli Sub-ODE Method through Bäcklund Transformation |
| title_full | Dynamics of the Traveling Wave Solutions of Fractional Date–Jimbo–Kashiwara–Miwa Equation via Riccati–Bernoulli Sub-ODE Method through Bäcklund Transformation |
| title_fullStr | Dynamics of the Traveling Wave Solutions of Fractional Date–Jimbo–Kashiwara–Miwa Equation via Riccati–Bernoulli Sub-ODE Method through Bäcklund Transformation |
| title_full_unstemmed | Dynamics of the Traveling Wave Solutions of Fractional Date–Jimbo–Kashiwara–Miwa Equation via Riccati–Bernoulli Sub-ODE Method through Bäcklund Transformation |
| title_short | Dynamics of the Traveling Wave Solutions of Fractional Date–Jimbo–Kashiwara–Miwa Equation via Riccati–Bernoulli Sub-ODE Method through Bäcklund Transformation |
| title_sort | dynamics of the traveling wave solutions of fractional date jimbo kashiwara miwa equation via riccati bernoulli sub ode method through backlund transformation |
| topic | fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equation Bäcklund transformation nonlinear differential equations exact solutions |
| url | https://www.mdpi.com/2504-3110/8/9/497 |
| work_keys_str_mv | AT mmossaalsawalha dynamicsofthetravelingwavesolutionsoffractionaldatejimbokashiwaramiwaequationviariccatibernoullisubodemethodthroughbacklundtransformation AT saimanoor dynamicsofthetravelingwavesolutionsoffractionaldatejimbokashiwaramiwaequationviariccatibernoullisubodemethodthroughbacklundtransformation AT mohammadalqudah dynamicsofthetravelingwavesolutionsoffractionaldatejimbokashiwaramiwaequationviariccatibernoullisubodemethodthroughbacklundtransformation AT musaadsaldhabani dynamicsofthetravelingwavesolutionsoffractionaldatejimbokashiwaramiwaequationviariccatibernoullisubodemethodthroughbacklundtransformation AT romanullah dynamicsofthetravelingwavesolutionsoffractionaldatejimbokashiwaramiwaequationviariccatibernoullisubodemethodthroughbacklundtransformation |