We used the unified method in this study to precisely solve the well-known the time fractional Drinfel'd-Sokolov-Wilson equation. The equation's graphic solution depicts a variety of physical phenomena, including periodic soliton behavior, a lump wave, a bright kink, a singular kink, a kink with interaction, and a kink with interaction. NLPDEs in mathematical physics and all other engineering fields can be solved using this method. It is a mathematical tool that is extremely potent and efficient.

References:

1.  Z.Y. Yan, H.Q. Zhang, On a new algorithm of constructing solitary wave solutions for systems of nonlinear evolution equations in mathematical physics, Appl. Math. Mech. 21 (4) (2000) 383–388.
2. M.L. Wang, Solitary wave solutions for variant Boussinesq equations, Phys. Lett. A 199 (34) (1995) 169–172.
3. M.R. Miura, Bäcklund Transformation, Springer-Verlag, Berlin, 1978.
4. E.G. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A 277 (2000) 212–218.

5. Sovon Chakraborty, Md. Obaidur Rahman F.M. Mehedi, "Sentiment Analysis on Twitter Tweets about COVID-19 vaccines Using NLP and Supervised KNN Classification Algorithm "  Indonesian Journal of Electronical Engineering and Computer Science. Vol. 23, No. 1, July 2021, pp. 463~470 ISSN: 2502-4752, DOI: 10.11591/ijeecs.v23.i1.pp463-470

6. Md. Obaidur Rahaman, Mohammod Abul Kashem, SC, F.M, S.M, F.K Internet of things based electrocardiogram monitoring system using machine learning algorithm, Article Published in International Journal of Advanced Computer Science and Applications(IJACSA) August, 2022.)

7. Muhammad Golam Kibria Md. Mamunur Rashid, Md. Obaidur Rahaman ,Al-Akhir Nayan, Sabrina Afrin, IoT based Smart Water Quality Prediction for Biofloc Aquaculture,IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 12, No. 6, 2021.

8. Obaidur Rahman, Mohammod Abul Kashem, Al-Akhir Nayan, Most. Fahmida, Fazly Rabbi, Marzia Ahmed, Mohammad Asaduzzaman “Internet of Things (IoT) Based ECG System for Rural Health Care”Article Published in International Journal of Advanced Computer Science and Applications(IJACSA), Volume 12 Issue 6, 2021.

9. Mohammod Obaidur Rahaman, Mohammod Abul Kashem and Mohammad Asaduzzaman Chowdhury. “ Analysis of Immunity System for Survival of COVID-19” Volume 2 - Issue 4, Mod Appl Pharm Pharmacol. 2(4). MAPP.000544.2021. DOI: 10.31031/MAPP.2021.02.000544. 

10. Al-Akhir Nayan; Muhammad Golam Kibria; Md. Obaidur Rahman; Joyeta Saha, “  River Water Quality Analysis and Prediction Using GBM” 2020 2nd International Conference on Advanced Information and Communication Technology (ICAICT), 2020, pp. 219-224, doi:10.1109/ICAICT51780.2020.9333492. ISBN:978-1-6654-2240-6. 

11. Marzia Ahmed, Mr. Obaidur Rahaman, Mostafijur Rahman and M. Abul Kashem “Analyzing the Quality of Water and Predicting the Suitability for Fish Farming in the Context of Bangladesh based on IoT” International Conference on Sustainable Technologies for Industry 4.0 (STI 2019) at Purbachal American City, Rupgonj, Bangladeh. [Scopus] 

12. Mohammod Obaidur Rahaman, Mohammod Abul Kashem “Cyber Physical System for Healthcare” International Journal of Advanced Research (IJAR), United Kingdom. November 2018. DOI URL: http://dx.doi.org/10.21474/IJAR01/7968,ISSN: 2320-5407 Int. J. Adv. Res. 6(10), 36-46.

13. Md. Obaidur Rahaman “Data and Information Security: A Modern Cryptographic Algorithm” International Journal of Advanced Research (IJAR), United Kingdom. October 2017. DOI URL: http://dx.doi.org/10.21474/IJAR01/5666, ISSN: 2320-5407 Int. J. Adv. Res. 5(10), 1508-1515

14. Md. Obaidur Rahaman, “Data and Information Security by using Elliptic Curve Cryptography” International Journal of Lambert Academic Publishing, July 2017.  ISBN(978-3-659-47487-3),P-ID(159172),Germany. https://www.morebooks.de/store/gb/book/1/isbn/978-3-659-47487-3,

15. “Data and Information Security in Modern World by using Elliptic Curve Cryptography” International Journal of Science and Academic Publishing, June 2017. p-ISSN: 2163-1484, e-ISSN: 2163-1492 2017; Vol 7 issue 2: page 29-44, USA.

16. Md. Obaidur Rahaman “Data and Information Security in Modern World” International Journal of Science and Academic Publishing, April 2017. p-ISSN: 2163-1484, e-ISSN: 2163-1492 2017; Vol 7 issue 1: page 12-21, USA.

17. Md. Obaidur Rahaman “Information Security: A Modern Cryptosystem of Symmetric and Asymmetric Key for Cyber Physical System” Journal of Applied Computer Science and Technology, Computer Engineering Division, IEB. http://www.iebbd.org/jcse/, Journal 2, Page no. 50-56.

18. Md. Obaidur Rahaman “Information security: A Modern cryptosystem of a public and a secret key“Multidisciplinary Journal of European University of Bangladesh. ISSN 2413-2632, Volume: 3, No: 3, January – June, 2018

19. A.M. Wazwaz, The tanh method for compact and noncompact solutions for variants of the KdV-Burger the K(nn) Burger equations, Physica D 213 (2006) 147–151.
20. M.Y. Wang, C.X. Yang, Extension on peaked wave solutions of CH-c equation, Chaos Soliton. Fract. 20 (2004) 815–825.
21. Z. Wen, Z. Liu, M. Song, New exact solutions for the classical Drinfel’d–Sokolov–Wilson equation, Appl. Math. Comput. 215 (2009) 2349–2358.
22. M.Y. Tang, R.Q. Wang, Z.J. Jing, Solitary waves and their bifurcations of KdV like equation with higher order nonlinearity, Sci. China Ser. A 45 (10) (2002) 1255–1267
23. S.K. Liu, Z.T. Fu, S.D. Liu, Q. Zhao, Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations, Phys. Lett. A 289 (2001) 69–74.
24. Z.T. Fu, S.K. Liu, S.D. Liu, Q. Zhao, New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations, Phys. Lett. A 290 (2001) 72–76.
25. R. Hirota, Exact solution of the KdV equation for multiple collisions of solitons, Phys. Rev. Lett. 27 (1971) 1192–1194.
26. Z. Fu, N. Yuan, Z. Chenb, J. Maoc, S. Liu, Multi-order exact solutions to the Drinfel’d–Sokolov–Wilson equations, Phys. Lett. A 373 (2009) 3710–3714.
27. Emine Misirli, Yusuf Gurefe, ‘Exact solutions of the Drinfel’d–Sokolov–Wilson equation using the Exp-function method’
28. R. Hirota, B. Grammaticos, A. Ramani, Soliton structure of the Drinfel’d–Sokolov–Wilson equation, J. Math. Phys. 27 (6) (1986) 1499–1505.
29. R.X. Yao, Z.B. Li, New exact solutions for three nonlinear evolution equations, Phys. Lett. A 297 (2002) 196–204.
30. C.P. Liu, X.P. Liu, Exact solutions of the classical Drinfel’d–Sokolov–Wilson equations and the relations among the solutions, Phys. Lett. A 303 (2002) 197–203.
31. E.G. Fan, An algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolution equations, J. Phys. A Math. Gen.36 (2003) 7009–7026
32. Y.Q. Yao, Abundant families of new traveling wave solutions for the coupled Drinfel’d–Sokolov–Wilson equation, Chaos Soliton. Fract. 24 (2005) 301–307.
33. M. Inc., On numerical doubly periodic wave solutions of the coupled Drinfel’d–Sokolov–Wilson equation by the decomposition method, Appl. Math. Comput. 172 (2006) 421–430.
34. Z.X. Qin, Z.H. Yan, An improved F-expansion method and its application to coupled Drinfel’d–Sokolov–Wilson equation, Commun. Theor. Phys. 50(2008) 309–314.