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

In this work, new analytic solutions for the nonlinear space-time fractional (3 + 1)-dimensional JimboMiwa equation and Burger-like equation including conformable derivative are obtained by using theG0/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 ofthe paper.

PDF

___

[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( ξ 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.

Mathematical Sciences and Applications E-Notes-Cover

ISSN: 2147-6268
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2013
Yayıncı: -

Arşiv