×
Ali, Khalid K.; Nuruddeen, R. I.; Raslan, K. R.

New structures for the space-time fractional simplified MCH and SRLW equations. (English) Zbl 1392.35326

Chaos Solitons Fractals 106, 304-309 (2018).
Summary: In this paper, we constructed new solitary structures for the space-time fractional simplified modified Camassa-Holm (MCH) equation and space-time fractional symmetric regularized long wave (SRLW) equation using the modified extended tanh method. The space-time fractional derivatives are defined in the sense of the new conformable fractional derivative. Further, with the help of Mathematica software, the set of over-determined algebraic equations obtained after reducing the equations to ordinary differentials equations are treated. We finally provide graphical illustrations for some structures.

Cited in 19 Documents

MSC:

35R11 Fractional partial differential equations
35C05 Solutions to PDEs in closed form

Keywords:

conformable fractional derivative; modified Camassa-Holm equation; symmetric regularized long wave equation; modified extended tanh method

Software:

Mathematica
Cite Review PDF
Full Text: DOI

References:

[1] Saha, R. S., New analytical exact solutions of time fractional KdV-KZK equation by kudryashov methods, Chin Phys B, 25, 040204, (2016)
[2] Kudryashov, N. A., One method for finding exact solutions of nonlinear differential equations, Commun Nonlinear Sci Numer Simul, 17, 11, 2248-2253, (2012) · Zbl 1250.35055
[3] Raslan, K. R.; Khalid, K. A.; Shallal, M. A., The modified extended tanh method with the Riccati equation for solving the space-time fractional EW and MEW equations, Chaos Solitons Fractals, 103, 404-409, (2017) · Zbl 1375.35608
[4] Bekir, A.; Guner, O. A., Exact solutions of nonlinear fractional differential equations by g’/g-expansion method, Chin Phys B, 22, 103, 404-409, (2013)
[5] Raslan, K. R.; Talaat, S. E.; Khalid, K. A., Numerical treatment for the coupled-BBM system, J Mod Methods Numer Math, 7, 2, 67-79, (2016) · Zbl 1356.65228
[6] Raslan, K. R.; Talaat, S. E.; Khalid, K. A., Application of septic b-spline collocation method for solving the coupled-BBM system, Appl Comput Math, 5, 5, 2-7, (2016)
[7] Khalid, K. A.; Raslan, K. R.; Talaat, S. E., Non-polynomial spline method for solving coupled Burgers equations, Comput Meth Differential Eq, 3, 3, 218-230, (2016) · Zbl 1412.65161
[8] Raslan, K. R.; Talaat, S. E.; Khalid, K. A., Collocation method with cubic trigonometric b-spline algorithm for solving coupled Burgers equations, Far East J Appl Math, 95, 2, 109-123, (2016) · Zbl 1360.35230
[9] Matinfar, M.; Eslami, M.; Kordy, M., The functional variable method for solving the fractional Korteweg-de Vries equations and the coupled Korteweg-de Vries equations, Pramana J Phys, 85, 583-592, (2015)
[10] Nuruddeen, R. I., Elzaki decomposition method and its applications in solving linear and nonlinear schrodinger equations, Sohag J Math, 4, 2, 1-5, (2017)
[11] Nuruddeen, R. I.; Nass, A. M., Exact solutions of wave-type equations by the aboodh decomposition method, Stochastic Model Appl, 21, 23-30, (2017)
[12] Bekir, A. E.; Guner, O. A., Exact solutions of distinct physical structures to the fractional potential Kadomtsev-Petviashvili equation, Commput Methods Differential Equations, 2, 26-36, (2014) · Zbl 1317.34006
[13] Bekir, A. E.; Guner, O. A., Analytical approach for the space-time nonlinear partial differential fractional equation, Int J Nonlinear Sci Numer Simul, 15, 463-470, (2014) · Zbl 1401.35310
[14] Kaplan, M. K.; Bekir, A. E., A novel analytical method for time-fractional differential equations, Int J Light Electron Opt, 127, 20, 8209-8214, (2016)
[15] Biswas, A., Topological solitons and other solutions to potential Korteweg-de-Vries equation, Rom Rep Phys, 65, 4, 1125-1137, (2013)
[16] Biswas, A., Topological soliton and other exact solutions to KdV-caudrey-dodd-gibbon equation, Results Math, 63, 1-2, 687-703, (2013) · Zbl 1418.37114
[17] Ahmad, Symmetry classifications and reductions of some classes of (2+1)-nonlinear heat equation, J Math Anlys and App, 339, 1, 175-181, (2008) · Zbl 1132.35044
[18] Biswas, A.; Kara, A. H.; Bokhari, A. H.; Zaman, F. D., Solitons and conservation laws of Klein-Gordon equation with power law and log law nonlinearities, Nonlinear Dyn, 73, 4, (2013) · Zbl 1281.35069
[19] Biswas, A.; Kara, A. H.; Moraru, L.; Zaman, F. D., Conservation laws of coupled Klein-Gordon equations with cubic and power law nonlinearities, Proceedings of the Romanian Academy-Series A, 15, 2, 123-129, (2014)
[20] Bakodah, H. O.; Al-Zaid, N. A.; Mirzazadeh, M.; Zhou, Q., Decomposition method for solving burger’s equation with Dirichlet and Neumann boundary conditions, Int J Light Electron Opt, 130, (2016)
[21] Bakodah, H.; Al Qarni, A. A.; Banaja, M.; Biswas, A., Bright and dark Thirring optical solitons with improved Adomian decomposition method, Int J Light Electron Opt, 130, (2016)
[22] Banaja, M.; Al Qarni, A. A.; Bakodah, H. O.; Biswas, A., Bright and dark solitons in cascaded system by improved Adomian decomposition scheme, Int J Light Electron Opt, 130, (2016)
[23] Khalid, K. A.; Nuruddeen, R. I., Analytical treatment for the conformable space-time fractional benney-luke equation via two reliable methods, Int J Phy Research, 5, 2, 109-114, (2017)
[24] Alquran, M.; Jaradat, H. M.; Syam, M. I., Analytical solution of the time-fractional phi-4 equation using modified power series method, Nonlinear Dyn, (2017) · Zbl 1394.35541
[25] Inc, M.; Yusuf, A.; Aliyu, A. I., Dark optical and other soliton solutions for the three different nonlinear schrodinger equations, Opt Quantum, 49, 11, (2017)
[26] Inc, M.; Yusuf, A.; Aliyu, A. I.; Baleanu, D., Optical soliton solutions for the higher-order dispersive cubic-quintic nonlinear schrodinger equation, Superlattice Microstruct, (2017)
[27] Baskonus, H. M.; Sulaiman, T. A.; Bulut, H., New solitary wave solutions to the (2+1)-dimensional Calogero-bogoyavlenskii-Schiff and the Kadomtsev-Petviashvili hierarchy equations, Indian J Phys, (2017)
[28] Islam, M. T.; Akbar, M. A.; Azad, M. A.K., A rational (g/g)-expansion method and its application to modified KdV-Burgers equation and the (2+1)-dimensional boussineq equation, Nonlinear Stud, 6, 4, (2015) · Zbl 1335.35018
[29] Bulu, H.; Sulaiman, T. A.; Erdogan, F.; Baskonus, H. M., On the new hyperbolic and trigonometric structures to the simplified MCH and SRLW equations, Eur Phys J Plus, 132, 350, (2017)
[30] Khalil, R.; Al Horani, M.; Yousef, A.; Sababheh, M., A new definition of fractional derivative, J Comput Appl Math, 265, 65-701, (2014) · Zbl 1297.26013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.