A Boiti-Leon Pimpinelli equations with time-conformable derivative

A Boiti-Leon Pimpinelli equations with time-conformable derivative

In this paper, we derive some new soliton solutions to (2 + 1)-Boiti-LeonPempinelli equations with conformable derivative by using an expansion technique based on the Sinh-Gordon equation. The obtained solutions have different expression such as trigonometric, complex and hyperbolic functions. Thispowerful and simple technique can be used to investigate solutions of othernonlinear partial differential equations.

___

  • 1] Singh, J., Kumar, D. & Kılıcman, A. (2013). Homotopy perturbation method for fractional gas dynamics equation using Sumudu transform. Abstract and Applied Analysis. Vol.2013.
  • [2] Ait Touchent, K. & Belgacem, F. (2015). Nonlinear fractional partial differential equations systems solutions through a hybrid homotopy perturbation Sumudu transform method. Nonlinear Studies, 22, 591-600.
  • [3] Dinkar, S., Singh, P. & Chauhan S. (2016). Homotopy Perturbation Sumudu Transform Method with He’s Polynomial for Solutions of Some Fractional Nonlinear Partial Differential Equations. International Journal of Nonlinear Science, 21, 91-97.
  • [4] Youssif, E., & Hamed, S. (2014). Solution of nonlinear fractional differential equations using the homotopy perturbation Sutransform method. Applied Mathematical Sciences, 8, 2195-2210.
  • [5] Buckwar, E. & Luchko, Y. (1988). Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations. J. Math. Anal.Appl., 227, 81-97.
  • [6] Hammouch, Z., Mekkaoui, T. & Agarwal, P. (2018). Optical solitons for the CalogeroBogoyavlenskii-Schiff equation in (2+1) dimensions with time-fractional conformable derivative. European Physical Journal Plus, 133:248.
  • [7] Manaf an, J. & Foroutan, M. (2016). Application of tan (φ(ξ)/2)-expansion method for solving the Biswas–Milovic equation for Kerr law nonlinearity. Optik-International Journal for Light and Electron Optics, 127, 2040-2054.
  • [8] Hammouch, Z. & Mekkaoui, T. (2012). Travelling-wave solutions for some fractional partial differential equation by means of generalized trigonometry functions. International Journal of Applied Mathematical Research, 1, 206-212.
  • [9] Rezazadeh, H., Korkmaz, A., Eslami, M., Vahidi, J., & Asghari, R. (2018). Traveling wave solution of conformable fractional generalized reaction Duffing model by generalized projective Riccati equation method. Optical and Quantum Electronics, 50(3), 150.
  • [10] Tasbozan, O., Cenesiz, Y., & Kurt, A. (2016). New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method. The European Physical Journal Plus, 131(7), 244.
  • [11] Zhu, J. & Ma, Z. (2005). An extended Jacobian elliptic function method for the discrete mKdV lattice. Chinese Physics, 14, 17.
  • [12] Hammouch, Z. & Mekkaoui, T. (2013). Approximate analytical and numerical solutions to fractional KPP-like equations. General Mathematics Notes, 14(2), 1-9.
  • [13] Hammouch, Z. & Mekkaoui, T. (2015). Control of a new chaotic fractional-order system using Mittag-Leffler stability. Nonlinear Studies, 22(4), 565-577.
  • [14] Hammouch, Z. & Mekkaoui, T. (2013). Approximate analytical solution to a timefractional Zakharov-Kuznetsov equation. Int. J. Eng. Tech., 1, 1-13.
  • [15] Mekkaoui, T. & Hammouch, Z. (2012) . Approximate analytical solutions to the BagleyTorvik equation by the Fractional Iteration Method. Annals of the University of CraiovaMathematics and Computer Science Series, 39(2), 251-256.
  • [16] Baskonus, H. et al. (2015). Active control of a chaotic fractional order economic system. Entropy, 17(8), 5771-5783.
  • [17] Yavuz, M. (2017). Novel solution methods for initial boundary value problems of fractional order with conformable differentiation. An International Journal of Optimization and Control: Theories & Applications, 8(1), 1-7.
  • [18] Yavuz, M. & Ozdemir N. (2017). New numerical techniques for solving fractional partial differential equations in conformable sense. Non-Integer Order Calculus and its Applications, Springer Cham., 49-62.
  • [19] Yavuz, M. & Yaskiran, B. (2018). Conformable derivative operator in modelling neuronal dynamics. Applications & Applied Mathematics, 13(2), 803-817.
  • [20] Yavuz, M. & Ozdemir N. (2018). On the solutions of fractional Cauchy problem featuring conformable derivative. ITM Web of Conferences, Vol. 22. EDP Sciences. [21] Yu, J., Liu, X. & Wang, T. (2010). Exact solutions and conservation laws of (2+ 1)-dimensional Boiti–Leon–Pempinelli equation. Applied Mathematics and Computation, 216(8), 2293-2300.
  • [22] Dai, C. & Wang, Y. (2009). Periodic structures based on variable separation solution of the (2+1)-dimensional Boiti–Leon–Pempinelli equation. Chaos, Solitons Fractals, 39, 350–355.
  • [23] Huang, D.J. & Zhang, H-Q. (2004). Exact travelling wave solutions for the Boiti–Leon–Pempinelli equation. Chaos Solitons and Fractals, 22, 243–247.
  • [24] Khalil, R., Al Horani, M., Yousef, A. & Sababheh, M. (2014). A new def nition of fractional derivative. Journal of Computational and Applied Mathematics, 264, 65-70.
  • [25] Yan, Z. (2003). A sinh-Gordon equation expansion method to construct doubly periodic solutions for nonlinear differential equations. Chaos, Solitons and Fractals, 16(2), 291-297.
  • [26] Qi, J., et al. (2014). Some new traveling wave exact solutions of the (2 + 1)-dimensional Boiti–Leon–Pempinelli equations.The Scientific World Journal, Vol.2014.