Analytical Solutions of Conformable Boussinesq-Double-Sinh-Gordon and First Boussinesq-Liouville Equations with the Help of Auxiulary Equation Method

Year 2020, Volume: 2 Issue: 2, 40 - 54, 30.10.2020

Sera Yılmaz Orkun Taşbozan

https://izlik.org/JA26UK77FL

Abstract

In this article, the analytical solutions of nonlinear fractional order Boussinesq-Double-Sinh-Gordon equation and first Boussinesq-Liouville equation are obtained with the aid of auxiulary equation method where the fractional derivatives are in conformable sense. Both equations were first converted to non-linear ordinary derivative differential equations with the help of wave transformation. auxiliary equation method was used to find analytical solutions of these ordinary derivative equations. Three dimensional graphics of the obtained results for nonlinear fractional order Boussinesq-Double-Sinh-Gordon equation and first Boussinesq-Liouville equation are given.

Keywords

Conformable Fractional Partial Differential Equations , Auxiulary Equation Method , Conformable Boussinesq-Double-Sinh-Gordon , Conformable First Boussinesq-Liouville

References

• Abdou, M. A., 2008. A generalized auxiliary equation method and its applications. Nonlinear Dynamics, 52(1-2): 95–102. Alhakim, L.A., Moussa, A.A., 2019. The double auxiliary equations method and its application to space-time fractional nonlinear equations. Journal of Ocean Engineering and Science, 4:7-13.
• Cenesiz, Y., Kurt, A., Tasbozan, O., 2017. On the New Solutions of the Conformable Time Fractional Generalized Hirota-Satsuma Coupled KdV System, Annals of West University of Timisoara-Mathematics and Computer Science, 55:37-50.
• Cenesiz, Y., Tasbozan, O., Kurt, A., 2017. Functional Variable Method for conformable fractional modified KdV-ZK equation and Maccari system. Tbilisi Mathematical Journal, 10(1): 118–126.
• Esen A. ve Tasbozan O., 2017. Numerical solution of time fractional Schrödinger equation by using quadratic B-spline finite elements, Annales Mathematicae Silesianae, 31: 83-98.
• Esen A., Karaagac B., Tasbozan O., 2017. Finite Difference Methods for Fractional Gas Dynamics Equation. Applied Mathematics & Information Sciences Letters, 4:1-4.
• Eslami, M., Rezazadeh, H., 2016. The first integral method for Wu–Zhang system with conformable time-fractional derivative. Calcolo, 53: 475–485.
• Jiong, S. ve Sirendaoreji, 2003. Auxiliary equation method for solving nonlinear partial differential equations. Physics Letters, 309:387-396.
• Khalil, R., Horani, M., Yousef, A., Sababheh, M., 2014. A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264:65-70.
• Korkmaz, A., Hosseini, K., 2017. Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable methods. Optical and Quantum Electronics, 49: 278.
• Taşbozan, O., Çenesiz, 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, 131:244.
• Taşbozan, O., Bayaslı, G., 2018. Numerical Solutions of Conformable Partial Differential Equations By Homotopy Analysis Method. Afyon Kocatepe University Journal of Science and Engineering, 18: 842-851.