Exact analytical soliton solutions of the M-fractional Akbota equation
Abstract In this paper we explore the new analytical soliton solutions of the truncated M-fractional nonlinear $$(1+1)$$ ( 1 + 1 ) -dimensional Akbota equation by applying the $$\exp _a$$ exp a function technique, Sardar sub-equation and generalized kudryashov techniques. Akbota is an integrable equ...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-06-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-64328-6 |
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| author | Muath Awadalla Aigul Taishiyeva Ratbay Myrzakulov Jihan Alahmadi Abdullah A. Zaagan Ahmet Bekir |
| author_facet | Muath Awadalla Aigul Taishiyeva Ratbay Myrzakulov Jihan Alahmadi Abdullah A. Zaagan Ahmet Bekir |
| author_sort | Muath Awadalla |
| collection | DOAJ |
| description | Abstract In this paper we explore the new analytical soliton solutions of the truncated M-fractional nonlinear $$(1+1)$$ ( 1 + 1 ) -dimensional Akbota equation by applying the $$\exp _a$$ exp a function technique, Sardar sub-equation and generalized kudryashov techniques. Akbota is an integrable equation which is Heisenberg ferromagnetic type equation and have much importance for the analysis of curve as well as surface geometry, in optics and in magnets. The obtained results are in the form of dark, bright, periodic and other soliton solutions. The gained results are verified as well as represented by two-dimensional, three-dimensional and contour graphs. The gained results are newer than the existing results in the literature due to the use of fractional derivative. The obtained results are very helpful in optical fibers, optics, telecommunications and other fields. Hence, the gained solutions are fruitful in the future study for these models. The used techniques provide the different variety of solutions. At the end, the applied techniques are simple, fruitful and reliable to solve the other models in mathematical physics. |
| format | Article |
| id | doaj-art-d2265680826b453c99760975871176af |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-d2265680826b453c99760975871176af2025-01-26T12:35:07ZengNature PortfolioScientific Reports2045-23222024-06-0114112110.1038/s41598-024-64328-6Exact analytical soliton solutions of the M-fractional Akbota equationMuath Awadalla0Aigul Taishiyeva1Ratbay Myrzakulov2Jihan Alahmadi3Abdullah A. Zaagan4Ahmet Bekir5Department of Mathematics and Statistics, College of Science, King Faisal UniversityRatbay Myrzakulov Eurasian International Centre for Theoretical PhysicsRatbay Myrzakulov Eurasian International Centre for Theoretical PhysicsDepartment of Mathematics, College of Science and Humanities in Al-Kharji, Prince Sattam Bin Abdulaziz UniversityDepartment of Mathematics, Faculty of Science, Jazan UniversityNeighbourhood of AkcaglanAbstract In this paper we explore the new analytical soliton solutions of the truncated M-fractional nonlinear $$(1+1)$$ ( 1 + 1 ) -dimensional Akbota equation by applying the $$\exp _a$$ exp a function technique, Sardar sub-equation and generalized kudryashov techniques. Akbota is an integrable equation which is Heisenberg ferromagnetic type equation and have much importance for the analysis of curve as well as surface geometry, in optics and in magnets. The obtained results are in the form of dark, bright, periodic and other soliton solutions. The gained results are verified as well as represented by two-dimensional, three-dimensional and contour graphs. The gained results are newer than the existing results in the literature due to the use of fractional derivative. The obtained results are very helpful in optical fibers, optics, telecommunications and other fields. Hence, the gained solutions are fruitful in the future study for these models. The used techniques provide the different variety of solutions. At the end, the applied techniques are simple, fruitful and reliable to solve the other models in mathematical physics.https://doi.org/10.1038/s41598-024-64328-6Fractional Akbota equation$$\exp _a$$ exp a function techniqueSardar sub-equation techniqueGeneralized Kudryashov techniqueAnalytical soliton solutions |
| spellingShingle | Muath Awadalla Aigul Taishiyeva Ratbay Myrzakulov Jihan Alahmadi Abdullah A. Zaagan Ahmet Bekir Exact analytical soliton solutions of the M-fractional Akbota equation Scientific Reports Fractional Akbota equation $$\exp _a$$ exp a function technique Sardar sub-equation technique Generalized Kudryashov technique Analytical soliton solutions |
| title | Exact analytical soliton solutions of the M-fractional Akbota equation |
| title_full | Exact analytical soliton solutions of the M-fractional Akbota equation |
| title_fullStr | Exact analytical soliton solutions of the M-fractional Akbota equation |
| title_full_unstemmed | Exact analytical soliton solutions of the M-fractional Akbota equation |
| title_short | Exact analytical soliton solutions of the M-fractional Akbota equation |
| title_sort | exact analytical soliton solutions of the m fractional akbota equation |
| topic | Fractional Akbota equation $$\exp _a$$ exp a function technique Sardar sub-equation technique Generalized Kudryashov technique Analytical soliton solutions |
| url | https://doi.org/10.1038/s41598-024-64328-6 |
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