1,481
Views
40
CrossRef citations to date
0
Altmetric
Research Articles

New exact solution for the (3+1) conformable space–time fractional modified Korteweg–de-Vries equations via Sine-Cosine Method

ORCID Icon, ORCID Icon & ORCID Icon
Pages 91-95 | Received 13 Aug 2018, Accepted 14 Oct 2018, Published online: 24 Oct 2018

References

  • Hereman W, Martino R, Miller J, et al. Exact solutions of nonlinear partial differential equations The tanh/sech method. Math. Visiting Scholar Grant Program Wolfram Research Inc., Champaign, Illinois. 2000;25:1–26.
  • Hereman W. Shallow water waves and solitary waves. In Mathematics of complexity and dynamical systems 2012 (pp. 1520–1532). Springer, New York, NY.
  • Wazwaz AM. Exact soliton and kink solutions for New (3+1)-dimensional nonlinear modified equations of wave propagation. Open Engineering. 2017;7(1):169–174. doi: 10.1515/eng-2017-0023
  • Khalil R, Al Horani M, Yousef A, et al. A new definition of fractional derivative. J Comput Appl Math. 2014;264:65–70. doi: 10.1016/j.cam.2014.01.002
  • Wazwaz AM. A sine-cosine method for handling nonlinear wave equations. Mathematical and Computer Modelling: An International Journal. 2004;40(5–6):499–508. doi: 10.1016/j.mcm.2003.12.010
  • Nuruddeen RI, Nass AM. Exact solutions of wave-type equations by the aboodh decomposition method. Stochastic Modelling and Applications. 2017;21(1):23–30.
  • Bekir AE, Guner OA. Analytical approach for the space– time nonlinear partial differential fractional equation. Int J Nonlinear Sci Numer Simul. 2014;15:463–470. doi: 10.1515/ijnsns-2013-0145
  • 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. 2015;85(4):583–592. doi: 10.1007/s12043-014-0912-5
  • Yaslan HC. New analytic solutions of the conformable space–time fractional kawahara equation. Int J Light Electron Optics. 2017;140:123–126. doi: 10.1016/j.ijleo.2017.04.015
  • Fan E. Extended tanh-function method and its applications to nonlinear equations. Phys Lett A. 2000;277(4–5):212–218. doi: 10.1016/S0375-9601(00)00725-8
  • Baleanu D, Aliyu AI, Yusuf A. Dark optical solitons and conservation laws to the resonance nonlinear shrödinger's equation with kerr law nonlinearity. Optik-International Journal for Light and Electron Optics. 2017;147:248–255. doi: 10.1016/j.ijleo.2017.08.080
  • Inc M, Yusuf A, Aliyu AI, et al. Fractional optical solitons for the conformable space–time nonlinear schrödinger equation with kerr law nonlinearity. Opt Quantum Electron. 2018;50:139. doi: 10.1007/s11082-018-1410-7
  • Mohyud-Din ST, Irshad A, Ahmed N, et al. Exact solutions of (3+1)-dimensional generalized KP equation arising in physics. Results Phys. 2017;7:3901–3909. doi: 10.1016/j.rinp.2017.10.007
  • Yaslan HC, Girgin E. New exact solutions for the conformable space-time fractional KdV, CDG, (2+1)-dimensional CBS and (2+1)-dimensional AKNS equations. Journal of Taibah University for Science. 2018;12:309–314. doi: 10.1080/16583655.2018.1469283
  • Seadawy AR, Lu D, Yue C. Travelling wave solutions of the generalized nonlinear fifth-order KdV water wave equations and its stability. Journal of Taibah University for Science. 2017;11:623–633. doi: 10.1016/j.jtusci.2016.06.002
  • Alam MN, Alam MM. An analytical method for solving exact solutions of a nonlinear evolution equation describing the dynamics of ionic currents along microtubules. Journal of Taibah University for Science. 2017;11:939–948. doi: 10.1016/j.jtusci.2016.11.004
  • Nuruddeen RI, Nass AM. Exact solitary wave solution for the fractional and classical GEW-burgers equations: an application of kudryashov method. Journal of Taibah University for Science. 2018;12:309–314. doi: 10.1080/16583655.2018.1469283