Analytical Solutions of Coupled Boiti-Leon-Pempinelli Equation with Fractional Derivative

Abstract

In this study, the sub-equation method is used as a tool for finding the analytical solutions of Coupled Boiti-Leon-Pempinelli (CBLP) equation where the derivatives are in conformable form with fractional term. In the introduction section advantages of the conformable derivative are expressed. By using the fractional wave transform and chain rule for conformable derivative, nonlinear fractional partial differential equation turns into nonlinear integer order differential equation. This translation gives us a great advantage for obtaining the analytical solutions and interpreting the physical behavior of the acquired solutions. As it can be in the rest of article sub-equation method is applied to CoupledBoiti-Leon-Pempinelli equation and the analytical results are derived successfully. This means that our method is effective and powerful for constructing exact and explicit analytic solutions to nonlinear PDEs with fractional term. While this process symbolic computation such as Mathematica is used. It is shown that, with the help of symbolic computation, sub-equation method ensures a powerful and straightforward mathematical tool for solving nonlinear partial differential equations.

Keywords

• Coupled Boiti-Leon-Pempinelli Equation
• Conformable Derivative
• Fractional Derivative
• Sub-Equation Method

Kaynakça

1. Az-Zo'bi EA, Alleddawi AO, Alsaraireh IW, Mamat M, Wrikat FD, Akinyemi L, Rezazadeh H. Novel solitons through optical fibers for perturbed cubic-quintic-septic nonlinear Schrdinger-type equation. International Journal of Nonlinear Analysis and Applications. 13(1), 2022, 2253--2266.
2. Siddique I, Jaradat MM, Zafar A, Mehdi KB, Osman MS. Exact traveling wave solutions for two prolific conformable M-Fractional differential equations via three diverse approaches. Results in Physics. 28, 2021, 104557.
3. N-Gbo NG, Xia Y. Traveling Wave Solution of Bad and Good Modified Boussinesq Equations with Conformable Fractional-Order Derivative. Qualitative Theory of Dynamical Systems. 21(1), 2022, 1--21.
4. Yokus A, Durur H, Abro KA. Symbolic computation of Caudrey-Dodd-Gibbon equation subject to periodic trigonometric and hyperbolic symmetries. The European Physical Journal Plus. 136(4), 2021, 1--16.
5. Saratha S R, Krishnan GSS, Bagyalakshmi M. Analysis of a fractional epidemic model by fractional generalised homotopy analysis method using modified Riemann-Liouville derivative. Applied Mathematical Modelling. 92, 2021, 525--545.
6. Jornet M. Uncertainty quantification for the random viscous Burgers' partial differential equation by using the differential transform method. Nonlinear Analysis. 209, 2021, 112340.
7. Zhang S, Zhang Y, Xu B. Exp-function Method and Reduction Transformations for Rogue Wave Solutions of the Davey-Stewartson Equations. Journal of Applied and Computational Mechanics. 7(1), 2021, 102--108.
8. Rahman Z, Ali MZ, Ullah MS. Analytical Solutions of Two Space-Time Fractional Nonlinear Models Using Jacobi Elliptic Function Expansion Method. Contemporary Mathematics. 2(3), 2021, 173--188.

9. Atangana A, Baleanu D, Alsaedi A. New properties of conformable derivative. Open Mathematics. 13(1), 2015, 889--898.
10. S. Zhang, H.Q. Zhang, Fractional sub-equation method and its applications to nonlinear fractional PDEs, Physics Letters A, 375 (7) (2011) 1069-1073.
11. Cenesiz Y, Kurt A, New fractional complex transform for conformable fractional partial differential equations. Journal of Applied Mathematics, Statistics and Informatics. 12(2) (2016) 41--47.
12. Khalil R, Al Horani M, Yousef A, Sababheh M. A new definition of fractional derivative. Journal of Computational and Applied Mathematics. 264 2014, 65--70.
13. Abdeljawad T. On conformable fractional calculus. Journal of Computational and Applied Mathematics. 279 (1), 2015, 57--66.
14. Malfliet W. Solitary wave solutions of nonlinear wave equations, American Journal of Physics. 60(7), 1992, 650--654.