AIMS Mathematics, 2020, 5(4): 3751-3761. doi: 10.3934/math.2020243

Research article

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

An application of improved Bernoulli sub-equation function method to the nonlinear conformable time-fractional SRLW equation

Department of Mathematics, Science and Letters Faculty, Mersin University, 33343, Mersin, Turkey

The nonlinear conformable time-fractional Symmetric Regularized Long Wave (SRLW) equation plays an important role in physics. This equation is an interesting model to describe ion-acoustic and space change waves with weak nonlinearity. In this paper, we solve the SRLW equation via the Improved Bernoulli Sub-Equation Function Method (IBSEFM). New exact solutions are constructed and by the aid of software mathematics programme, 2D and 3D graphs of the solutions according to the parameters are plotted. The results show that IBSEFM is a powerful mathematical tool to solve nonlinear conformable time-fractional equations arising in mathematical physics.
  Figure/Table
  Supplementary
  Article Metrics

References

1. F. Maucher, D. Buccoliero, S. Skupin, et al. Tracking azimuthons in nonlocal nonlinear media, Opt. Quant. Electron., 41 (2009), 337-348.    

2. M. Alidou, A. Kenfack-Jiotsa, T. C. Kofane, Modulational instability and spatiotemporal transition to chaos, Chaos, Solitons Fractals, 27 (2006), 914-925.    

3. R. Nath, P. Pedri, L. Santos, Stability of Dark Solitons in Three Dimensional Dipolar Bose-Einstein Condensates, Phys. Rev. Lett., 101 (2008), 210402.

4. M. G. Prahović, R. D. Hazeltine, P. J. Morrison, Exact solutions for a system of nonlinear plasma fluid equations, Physics of Fluids B: Plasma Physics, 4 (1992), 831-840.    

5. P. B. Ndjoko, J. M. Bilbault, S. Binzcak, et al. Compact-envelope bright solitary wave in a DNA double strand, Phys. Rev. E, 85 (2012).

6. S. B. Yamgoue, F. B. Pelap, Comment on Compact envelope dark solitary wave in a discrete nonlinear electrical transmission line, Phys. Lett. A., 380 (2016), 2017-2020.    

7. G. R. Deffo, S. B. Yamgoue, F. B. Pelap, Modulational instability and peak solitary wave in a discrete nonlinear electrical transmission line described by the modified extended nonlinear Schrodinger equation, The Eurupean Phys. J., 91 (2018).

8. E. Kengne, R. Vaillancourt, Transmission of solitary pulse in dissipative nonlinear transmission lines, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), 3804-3810.    

9. E. Fan, Y. C. Hon, Applications of extended tanh method to special types of nonlinear equations, Appl. Math. Comput., 141 (2003), 351-358.

10. A. M. Wazwaz, The extended tanh method for abundant solitary wave solutions of nonlinear wave equations, Appl. Math. Comput., 187 (2007), 1131-1142.

11. Z. Feng, On explicit exact solutions to the compound Burgers-Kdv equation, Phys. Lett., 293 (2002), 57-66.    

12. K. Hosseini, P. Gholamin, Feng's first integral method for analytic treatment of two higher dimensional nonlinear partial differantial equations, Differantial Equations and Dynamical Systems, 23 (2015), 317-325.

13. A. M. Wazwaz, Sine-cosine method for handling nonlinear wave equations, Math. Comput. Model., 40 (2004), 499-508.

14. Y. Fu, J. Li, Exact stationary-wave solutions in the standart model of the Kerr-nonlinear optical fiber with the Bragggrating, J. Appl. Anal. Comput., 7 (2017), 1177-1184.

15. N. Tanghizadeh, M. Mirzazadeh, A. S. Paghaleh, et al. Exact solutions of nonlinear evolution equations by using the modified simple equation method, Ain Shams Eng. J., 3 (2012), 321-325.    

16. M. Mirzazadeh, Modified simple equation method and its applications to nonlinear partial differantial equations, Inf. Sci. Lett., 3 (2014), 1-9.    

17. A. J. M. Jawad, Soliton solutions for nonlinear systems (2+1) dimensional equations, IOSR Journal of Mathematics, 1 (2012), 27-34.

18. I. E. Inan, D. Kaya, Exact solutions of some nonlinear partial differential equations, Physica A, 381 (2007), 104-115.    

19. M. A. Akbar, N. H. M. Ali, The improved F-expansion method with Riccati equation and its applications in mathematical physics, Cogent Mathematics, 4 (2017), 1-19.

20. Y. M. Zhao, F-expansion method and its application for finding new exact solutions to the Kudryashov-Sinelshchikov equation, J. Appl. Math., 2013 (2013).

21. F. Ozpinar, H. M. Baskonus, H. Bulut, On the complex and hyperbolic structures for the (2+1)- dimensional boussinesq water equation, Entropy, 17 (2015), 8267-8277.

22. H. M. Baskonus, M. Askin, Travelling Wave Simulations to the Modified Zakharov-Kuzentsov Model Arising In Plasma Physics, 6th International Youth Science Forum, Computer Science and Engineering, (2016) Lviv, Ukraine, 24-26 November.

23. H. M. Baskonus, H. Bulut, Exponential prototype structure for (2+1) dimensional Boiti Leon Pempinelli systems in mathematical physics, Waves Random Complex Media, 26 (2016), 189-196.    

24. F. Dusunceli, Solutions for the Drinfeld-Sokolov Equation Using an IBSEFM Method, MSU Journal of Science, J. Amer. Math. Soc., 6 (2018), 505-510.

25. W. Liu and K. Chen, The functional variable method for finding exact solutions of some nonlinear timefractional differential equations, Pramana, 81 (2013), 377-384.    

26. B. Lu, The first integral method for some time fractional diferential equations, J. Math. Anal. Appl., 395 (2012), 684-693.    

27. Z. Bin, Exp-function method for solving fractional partial dierential equations, The Sci. World J., 2013 (2013), 1-8.

28. A. Emad, B. Abdel-Salam, A. Y. Eltayeb, Solution of nonlinear space-time fractional diffeerential equations using the fractional Riccati expansion method, Math. Probl. Eng., 2013 (2013), 1-6.

29. H. Bulut, G. Yel, H. M. Baskonus, An Application of Improved Bernoulli Sub-Equation Function Method to The Nonlinear Time-Fractional Burgers Equation, Turk. J. Math. Comput. Sci., 5 (2016), 1-7.

30. D. G. Prakasha, P. Veeresha, H. M. Baskonus, Analysis of the dynamics of hepatitis E virus using the Atangana-Baleanu fractional derivative, The European Physical Journal Plus, 134 (2019), 241.

31. R. Khalil, M. Al Horani, A. Yousef, et al. A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65-70.    

32. T. Abdeljawad, On conformable fractional calulus, J. Comput. Appl. Math., 279 (2015), 57-66.

33. A. Atangana, D. Baleanu, A. Alsaedi, New properties of conformable derivative, Open Math., 13 (2015), 1-10.

34. A. Atangana, A novel model for the lassa hemorrhagic fever, deathly disease for pregnant women, Neural. Comput. Appl., 26 (2015), 1895-1903.    

35. A. Korkmaz, K. Hosseini, Exact solutions of a nonlinear conformable time fractional parabolic equation with exponential nonlinearity using reliable methods, Opt. Quant. Electron., 49 (2017), 278.

36. A. Korkmaz, Exact solutions of space-time fractional EW and modified EW equations, Chaos, Solitons Fractals, 96 (2017), 132-138.    

37. A. Korkmaz, Exact solutions to (3 + 1) conformable time fractional Jimbo-Miwa, ZakharovKuznetsov and modified Zakharov-Kuznetsov equations, Commun. Theor. Phys., 67 (2017), 479-482.    

38. K. Hosseini, R. Ansari, New exact solutions of nonlinear conformable timefractional Boussinesq equations using the modified Kudryashov method, Waves Random Complex Media, 27 (2017), 628-636.    

39. D. Kumar, J. Singh, D. Baleanu, Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel, Physica A, 492 (2018), 155-167.    

40. D. Kumar, J. Singh, D. Baleanu, A new analysis for fractional model of regularized long wave equation arising in ion acoustic plasma waves, Math. Methods Appl. Sci., 40 (2017), 5642-5653.

41. T. A. Sulaiman, M. Yavuz, H. Bulut, et al. Investigation of the fractional coupled viscous Burgers' equation involving Mittag-Leffler kernel, Physica A: Statistical Mechanics and its Applications, 527 (2019), 121-126.

42. H. Rezazadeh, D. Kumar, T. A. Sulaiman, et al. New complex hyperbolic and trigonometric solutions for the generalized conformable fractional Gardner equation, Mod. Phys. Lett. B, 33 (2019), 1950196.

43. H. Rezazadeh, A. Korkmaz, M. Eslami, et al. Traveling wave solution of conformable fractional generalized reaction Duffing model by generalized projective Riccati equation method, Opt. Quant. Electron., 50 (2018), 150.

44. G. Yel, H. M. Baskonus, Solitons in conformable time-fractional Wu-Zhang system arising in coastal design, Pramana, 93 (2019), 57.

45. C. E. Seyler, D. L. Fenstermacher, A symmetric regularized-long-wave equation, Phys. Fluids, 27 (1984), 4-7.

46. R. I. Nuruddeen, A. M. Nass, Exact solitary wave solution for the fractional and classical GEWBurgers equations: an application of Kudryashov method, Journal of Taibah University for Science, 12 (2018), 309-314.    

47. K. K. Ali, R. I. Nuruddeen, K. R. Raslan, New structures for the space-time fractional simplified MCH and SRLW equations, Chaos Soliton. Fractal., 106 (2018), 304-309.    

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved