Exact Solitary Wave Solutions and Sensitivity Analysis of the Fractional (3+1)D KdV–ZK Equation
The present paper examines a novel exact solution to nonlinear fractional partial differential equations (FDEs) through the Sardar sub-equation method (SSEM) coupled with Jumarie’s Modified Riemann–Liouville derivative (JMRLD). We take the (3+1)-dimensional space–time fractional modified Korteweg-de...
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| Language: | English |
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MDPI AG
2025-07-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/7/476 |
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| author | Asif Khan Fehaid Salem Alshammari Sadia Yasin Beenish |
| author_facet | Asif Khan Fehaid Salem Alshammari Sadia Yasin Beenish |
| author_sort | Asif Khan |
| collection | DOAJ |
| description | The present paper examines a novel exact solution to nonlinear fractional partial differential equations (FDEs) through the Sardar sub-equation method (SSEM) coupled with Jumarie’s Modified Riemann–Liouville derivative (JMRLD). We take the (3+1)-dimensional space–time fractional modified Korteweg-de Vries (KdV) -Zakharov-Kuznetsov (ZK) equation as a case study, which describes some intricate phenomena of wave behavior in plasma physics and fluid dynamics. With the implementation of SSEM, we yield new solitary wave solutions and explicitly examine the role of the fractional-order parameter in the dynamics of the solutions. In addition, the sensitivity analysis of the results is conducted in the Galilean transformation in order to ensure that the obtained results are valid and have physical significance. Besides expanding the toolbox of analytical methods to address high-dimensional nonlinear FDEs, the proposed method helps to better understand how fractional-order dynamics affect the nonlinear wave phenomenon. The results are compared to known methods and a discussion about their possible applications and limitations is given. The results show the effectiveness and flexibility of SSEM along with JMRLD in forming new categories of exact solutions to nonlinear fractional models. |
| format | Article |
| id | doaj-art-59e6bb47a86044688016c9f853fa9291 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-59e6bb47a86044688016c9f853fa92912025-08-20T03:36:14ZengMDPI AGFractal and Fractional2504-31102025-07-019747610.3390/fractalfract9070476Exact Solitary Wave Solutions and Sensitivity Analysis of the Fractional (3+1)D KdV–ZK EquationAsif Khan0Fehaid Salem Alshammari1Sadia Yasin2Beenish3Department of Mathematics, University of Malakand, Chakdara 18800, PakistanDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi ArabiaDepartment of Mathematics, Government College University, Faisalabad 38000, PakistanDepartment of Mathematics, Quaid-I-Azam University, Islamabad 45320, PakistanThe present paper examines a novel exact solution to nonlinear fractional partial differential equations (FDEs) through the Sardar sub-equation method (SSEM) coupled with Jumarie’s Modified Riemann–Liouville derivative (JMRLD). We take the (3+1)-dimensional space–time fractional modified Korteweg-de Vries (KdV) -Zakharov-Kuznetsov (ZK) equation as a case study, which describes some intricate phenomena of wave behavior in plasma physics and fluid dynamics. With the implementation of SSEM, we yield new solitary wave solutions and explicitly examine the role of the fractional-order parameter in the dynamics of the solutions. In addition, the sensitivity analysis of the results is conducted in the Galilean transformation in order to ensure that the obtained results are valid and have physical significance. Besides expanding the toolbox of analytical methods to address high-dimensional nonlinear FDEs, the proposed method helps to better understand how fractional-order dynamics affect the nonlinear wave phenomenon. The results are compared to known methods and a discussion about their possible applications and limitations is given. The results show the effectiveness and flexibility of SSEM along with JMRLD in forming new categories of exact solutions to nonlinear fractional models.https://www.mdpi.com/2504-3110/9/7/476Sardar sub-equation methodobtain exact solutions for nonlinear fractional partial differential equationssensitivity analysis |
| spellingShingle | Asif Khan Fehaid Salem Alshammari Sadia Yasin Beenish Exact Solitary Wave Solutions and Sensitivity Analysis of the Fractional (3+1)D KdV–ZK Equation Fractal and Fractional Sardar sub-equation method obtain exact solutions for nonlinear fractional partial differential equations sensitivity analysis |
| title | Exact Solitary Wave Solutions and Sensitivity Analysis of the Fractional (3+1)D KdV–ZK Equation |
| title_full | Exact Solitary Wave Solutions and Sensitivity Analysis of the Fractional (3+1)D KdV–ZK Equation |
| title_fullStr | Exact Solitary Wave Solutions and Sensitivity Analysis of the Fractional (3+1)D KdV–ZK Equation |
| title_full_unstemmed | Exact Solitary Wave Solutions and Sensitivity Analysis of the Fractional (3+1)D KdV–ZK Equation |
| title_short | Exact Solitary Wave Solutions and Sensitivity Analysis of the Fractional (3+1)D KdV–ZK Equation |
| title_sort | exact solitary wave solutions and sensitivity analysis of the fractional 3 1 d kdv zk equation |
| topic | Sardar sub-equation method obtain exact solutions for nonlinear fractional partial differential equations sensitivity analysis |
| url | https://www.mdpi.com/2504-3110/9/7/476 |
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