(G'/G)-expansion Method for the Conformable space-time Fractional Jimbo-Miwa and Burger-like Equations

Year 2019, Volume: 7 Issue: 1, 47 - 53, 30.04.2019

H. Çerdik Yaslan , Ayşe Girgin

Abstract

In this work, new analytic solutions for the nonlinear space-time fractional (3 + 1)-dimensional Jimbo-

Miwa equation and Burger-like equation including conformable derivative are obtained by using the

(G'/G) expansion method. The obtained traveling wave solutions are represented by the hyperbolic,

trigonometric and rational functions. Simulations of the obtained solutions are presented at the end of

the paper.

Keywords

The space time fractional (3 + 1)-dimensional Jimbo-Miwa equation, The space time fractional Burger-like equation, Conformable derivative, (G'/G) expansion method; Traveling wave solutions

References

• [1] Esen, A., Sulaiman, T. A., Bulut, H., Ba¸skonu¸s, H.M., Optical solitons to the space-time fractional (1+1)- dimensional coupled nonlinear Schrodinger equation. Optik. 167 (2018) 150-156.
• [2] Ba¸skonu¸s, H. M., Bulut, H., Regarding on the prototype solutions for the nonlinear fractional-order biological population model. Regarding on the prototype solutions for the nonlinear fractional-order biological population model. AIP Conference Proceedings 1738 (2016) 290004.
• [3] Firoozjaee, M.A., Yousefi, S.A., A numerical approach for fractional partial differential equations by using Ritz approximation. Appl. Math. Comput. 338 (2018) 711-721.
• [4] Dehestani, H., Ordokhani, Y., Razzaghi, M., Fractional-order Legendre-Laguerre functions and their applications in fractional partial differential equations. Appl. Math. Comput. 336 (2018) 433-453.
• [5] Feng, Q., A new approach for seeking coefficient function solutions of conformable fractional partial differential equations based on the Jacobi elliptic equation. Chinese J. Phys. 56 (2018) 2817-2828
• [6] Ziane, D., Baleanu, D., Belghaba, K., Hamdi Cherif, M., Local fractional Sumudu decomposition method for linear partial differential equations with local fractional derivative. J. King Saud Univ. Sci. 31 (2019) 83-88.
• [7] Khader, M.M., Saad, K. M., A numerical approach for solving the fractional Fisher equation using Chebyshev spectral collocation method. Chaos Soliton Fract. 110 (2018) 169-177.
• [8] Zhang, S., Hong, S., Variable separation method for a nonlinear time fractional partial differential equation with forcing term. J. Comput. Appl. Math. 339 (2018) 297-305.
• [9] Nagy, A. M., Numerical solution of time fractional nonlinear Klein-Gordon equation using Sinc-Chebyshev collocation method. Appl.Math.Comput. 310 (2017) 139-148.
• [10] Yusuf, A., ˙Inc, M., Aliyu, A. I., Baleanu, D., Efficiency of the new fractional derivative with nonsingular Mittag-Leffler kernel to some nonlinear partial differential equations. Chaos Soliton Fract. 116 (2018) 220-226.
• [11] Chen, C., Jiang, Y. L., Simplest equation method for some time-fractional partial differential equations with conformable derivative. Comput. Math. Appl. 75 (2018) 2978-2988.
• [12] Mohammadi, F., Cattani, C., A generalized fractional-order Legendre wavelet Tau method for solving fractional differential equations. J. Comput. Appl. Math. 339 (2018) 306-316.
• [13] Jimbo, M., Miwa, T., Solitons and infinite dimensional Lie algebras. Publ. RIMS. Kyoto Univ. 19 (1983) 943-1001.
• [14] Dorizzi, B., Grammaticos, B., Ramani, A.,Winternitz, P., Are all the equations of the Kadomtsev-Petviashvili hierarchy integrable? J. Math. Phys. 12 (1986) 2848-2852.
• [15] Wazwaz, A. M., Multiple-soliton solutions for the Calogero-Bogoyavlenskii-Schiff, Jimbo-Miwa and YTSF equations. Appl. Math. Comput. 203 (2008) 592-597.
• [16] Ali, K. K., Nuruddeen, R. I., Hadhoud, A. R., New exact solitary wave solutions for the extended (3 + 1)- dimensional Jimbo-Miwa equations. Results Phys. 9 (2018) 12-16.
• [17] Mehdipoor, M., Neirameh, A., New soliton solutions to the (3+1)-dimensional Jimbo-Miwa equation. Optik. 126 (2015) 4718-4722.
• [18] Özi¸s, T., Aslan, I., Exact and explicit solutions to the (3 +1)-dimensional Jimbo-Miwa equation via the Expfunction method. Phys. Lett. A 372 (2008) 7011-7015.
• [19] Li, Z., Dai, Z., Liu, J., Exact three-wave solutions for the (3 + 1)-dimensional Jimbo-Miwa equation. Comput Math Appl. 61 (2011) 2062-2066.
• [20] Kolebaje, O. T., Popoola, O. O., Exact Solution of Fractional STO and Jimbo-Miwa Equations with the Generalized Bernoulli Equation Method. The African Review of Physics (2014) 9-0026.
• [21] Sirisubtawee, S., Koonprasert, S., Khaopant, C., Porka, W., Two Reliable Methods for Solving the (3 + 1)- Dimensional Space-Time Fractional Jimbo-Miwa Equation. Math. Probl. Eng. 2017 (2017) 1-30.
• [22] Korkmaz, A., Exact Solutions to (3+1) Conformable Time Fractional Jimbo-Miwa, Zakharov-Kuznetsov and Modifed Zakharov-Kuznetsov Equations. Commun. Theor. Phys. 67 (2017) 479-482.
• [23] Rawashdeh, M. S., A reliable method for the space-time fractional Burgers and time-fractional Cahn-Allen equations via the FRDTM. Adv. Differ. Equ. 99 (2017) 1-14.
• [24] Bulut, H., Tuz, M., Aktürk, T., New multiple solution to the Boussinesq equation and the Burgers-like equation. J. Appl. Math. 952614 (2013) 1-6.
• [25] Wang, X.M., Bilige, S.D., Bai, Y.X., A General Sub-Equation Method to the Burgers-Like Equation. Thermal Science 21 (2017) 1681-1687.
• [26] ˙Inan, I. E., Duran, S., U˘gurlu, Y., tan(F( 2 ))-expansion method for traveling wave solutions of AKNS and Burgers-like equations Modified method of simplest equation and its applications to the Bogoyavlenskii equation. Optik. 138 (2017) 15-20.
• [27] ˙Inc, M., The approximate and exact solutions of the space and time-fractional Burgers equations with initial conditions by variational iteration method. J. Math. Anal. Appl. 345 (2008) 476-484.
• [28] Khalil, R., Horani, M. A., Yousef, A., Sababheh, M., A new defnition of fractional derivative. J. Comput. Appl. Math. 264 (2014) 65-70.