Exploring the new soliton solutions to the nonlinear M-fractional evolution equations in shallow water by three analytical techniques
This paper explores the new soliton solutions of the evolution equations named as truncated M-fractional (1+1)-dimensional non-linear Kaup-Boussinesq system by utilizing the expa function, modified simplest equation and Sardar sub-equation techniques. This system is used in the analysis of long wave...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-11-01
|
| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723008859 |
| _version_ | 1797615912551972864 |
|---|---|
| author | Asim Zafar M. Raheel Ali M. Mahnashi Ahmet Bekir Mohamed R. Ali A.S. Hendy |
| author_facet | Asim Zafar M. Raheel Ali M. Mahnashi Ahmet Bekir Mohamed R. Ali A.S. Hendy |
| author_sort | Asim Zafar |
| collection | DOAJ |
| description | This paper explores the new soliton solutions of the evolution equations named as truncated M-fractional (1+1)-dimensional non-linear Kaup-Boussinesq system by utilizing the expa function, modified simplest equation and Sardar sub-equation techniques. This system is used in the analysis of long waves in shallow water. The attained results involving trigonometric, hyperbolic and exponential functions. The effect of fractional order derivative is also discussed. Obtained results are very close to the approximate results due to the use of M-fractional derivative. Achieved results are verified by Mathematica tool. Few of the gained results are also explained through 2-D, 3-D and contour graphs. At the end, these techniques are straight forward, useful and effective to deal with non-linear FPDEs. |
| first_indexed | 2024-03-11T07:33:43Z |
| format | Article |
| id | doaj.art-3ad16fada2bd41b1abc7e3fb6629b9e9 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-11T07:33:43Z |
| publishDate | 2023-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-3ad16fada2bd41b1abc7e3fb6629b9e92023-11-17T05:26:31ZengElsevierResults in Physics2211-37972023-11-0154107092Exploring the new soliton solutions to the nonlinear M-fractional evolution equations in shallow water by three analytical techniquesAsim Zafar0M. Raheel1Ali M. Mahnashi2Ahmet Bekir3Mohamed R. Ali4A.S. Hendy5Department of Mathematics, COMSATS University Islamabad, Vehari Campus, PakistanDepartment of Mathematics, COMSATS University Islamabad, Vehari Campus, PakistanDepartment of Mathematics, College of Science, Jazan University, Jazan, Saudi ArabiaNeighbourhood of Akcaglan, Imarli Street, Number: 28/4, 26030, Eskisehir, TurkeyBasic Engineering Science Department, Benha Facultyv of Engineering, Benha University, Benha, Egypt; Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, Egypt; Corresponding author.Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., 620002, Yekaterinburg, RussiaThis paper explores the new soliton solutions of the evolution equations named as truncated M-fractional (1+1)-dimensional non-linear Kaup-Boussinesq system by utilizing the expa function, modified simplest equation and Sardar sub-equation techniques. This system is used in the analysis of long waves in shallow water. The attained results involving trigonometric, hyperbolic and exponential functions. The effect of fractional order derivative is also discussed. Obtained results are very close to the approximate results due to the use of M-fractional derivative. Achieved results are verified by Mathematica tool. Few of the gained results are also explained through 2-D, 3-D and contour graphs. At the end, these techniques are straight forward, useful and effective to deal with non-linear FPDEs.http://www.sciencedirect.com/science/article/pii/S2211379723008859Space–time fractional Kaup–Boussinesq systemThe expa function techniqueModified simplest equation techniqueSardar sub-equation techniqueNew soliton solutions |
| spellingShingle | Asim Zafar M. Raheel Ali M. Mahnashi Ahmet Bekir Mohamed R. Ali A.S. Hendy Exploring the new soliton solutions to the nonlinear M-fractional evolution equations in shallow water by three analytical techniques Results in Physics Space–time fractional Kaup–Boussinesq system The expa function technique Modified simplest equation technique Sardar sub-equation technique New soliton solutions |
| title | Exploring the new soliton solutions to the nonlinear M-fractional evolution equations in shallow water by three analytical techniques |
| title_full | Exploring the new soliton solutions to the nonlinear M-fractional evolution equations in shallow water by three analytical techniques |
| title_fullStr | Exploring the new soliton solutions to the nonlinear M-fractional evolution equations in shallow water by three analytical techniques |
| title_full_unstemmed | Exploring the new soliton solutions to the nonlinear M-fractional evolution equations in shallow water by three analytical techniques |
| title_short | Exploring the new soliton solutions to the nonlinear M-fractional evolution equations in shallow water by three analytical techniques |
| title_sort | exploring the new soliton solutions to the nonlinear m fractional evolution equations in shallow water by three analytical techniques |
| topic | Space–time fractional Kaup–Boussinesq system The expa function technique Modified simplest equation technique Sardar sub-equation technique New soliton solutions |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723008859 |
| work_keys_str_mv | AT asimzafar exploringthenewsolitonsolutionstothenonlinearmfractionalevolutionequationsinshallowwaterbythreeanalyticaltechniques AT mraheel exploringthenewsolitonsolutionstothenonlinearmfractionalevolutionequationsinshallowwaterbythreeanalyticaltechniques AT alimmahnashi exploringthenewsolitonsolutionstothenonlinearmfractionalevolutionequationsinshallowwaterbythreeanalyticaltechniques AT ahmetbekir exploringthenewsolitonsolutionstothenonlinearmfractionalevolutionequationsinshallowwaterbythreeanalyticaltechniques AT mohamedrali exploringthenewsolitonsolutionstothenonlinearmfractionalevolutionequationsinshallowwaterbythreeanalyticaltechniques AT ashendy exploringthenewsolitonsolutionstothenonlinearmfractionalevolutionequationsinshallowwaterbythreeanalyticaltechniques |