SITEM for the Conformable Space-Time Fractional Coupled KD Equations

Yıl 2018, Cilt: 3 Sayı: 3, 223 - 233, 29.12.2018

Handan Yaslan Ayşe Girgin

https://doi.org/10.30931/jetas.452732

Cited By: 1

Öz

In the present paper, new analytical solutions for the space-time fractional coupled Konopelchenko-Dubrovsky (KD) equations are obtained by using the simplified $\tan(\frac{\phi (\xi) }{2})$-expansion method (SITEM). Here, fractional derivatives are described in conformable sense. The obtained traveling wave solutions are expressed by the trigonometric, hyperbolic, exponential and rational functions. Simulation of the obtained solutions are given at the end of the paper.

Anahtar Kelimeler

Space-time fractional coupled KD equations, Simplified $\tan(\frac{\phi (\xi) }{2})$-expansion method (SITEM), Conformable derivative.

Kaynakça

• [1] Dehghan, M., Manafian, J., ‘‘The Solution of the Variable Coefficients Fourth- Order Parabolic Partial Differential Equations by the Homotopy Perturbation Method.’’ Zeitschrift für Naturforschung A. 64. 7-8 (2009): 420-430.
• [2] Dehghan, M., Manafian J., Saadatmandi, A., ‘‘Solving Nonlinear Fractional Partial Differential Equations Using the Homotopy Analysis Method.’’ Num. Meth. Partial Differential Eq.: An International Journal 26.2 (2010): 448-479.
• [3] Dehghan, M., Manafian, J., Saadatmandi, A., ‘‘Analytical treatment of some partial differential equations arising in mathematical physics by using the Exp-function method.’’ Int. J. Modern Phys. B 25.22 (2011): 2965-2981.
• [4] Foroutan, M., Zamanpour, I., Manafian, J., ‘‘Applications of IBSOM and ETEM for solving the nonlinear chains of atoms with long-range interactions.’’ Eur. Phys. J. Plus 132.10 (2017): 421.
• [5] Seyedi, S. H., Saray, B. N., Nobari, M. R. H., ‘‘Using interpolation scaling functions based on Galerkin method for solving non-Newtonian fluid flow between two vertical flat plates.’’ Appl. Math. Comput. 269 (2015): 488-496.
• [6] Seyedi, S. H., Saray, B. N., Ramazani, A., ‘‘On the multiscale simulation of squeezing nanofluid flow by a highprecision scheme.’’ Powder Technology 340 (2018): 264-273.
• [7] Konopelchenko, B. G., Dubrovsky, V. G., ‘‘Some new integrable nonlinear evolution equations in (2+1)-dimensions.’’ Phys. Lett. 102 (1984): 15-17.
• [8] Ji, L., Sen-Yue, L, Ke-Lin, W., ‘‘Multi-soliton solutions of the Konopelchenko-Dubrovsky equation.’’ Chin. Phys. Lett. 18.9 (2001): 1173.
• [9] Song, L., Zhang, H., ‘‘Application of the extended homotopy perturbation method to a kind of nonlinear evolution equations.’’ Appl. Math. Comput. 197.1 (2008): 87-95.
• [10] Zhang, S., Xia, T., ‘‘A generalized F-expansion method and new exact solutions of Konopelchenko–Dubrovsky equations.’’ Appl. Math. Comput. 183.2 (2006): 1190-1200.
• [11] Yasar, E, Giresunlu, I. B., ‘‘Exact Traveling Wave Solutions and Conservation Laws of (2+1) Dimensional Konopelchenko-Dubrovsky System.’’ IJNS 22.2 (2016): 118-128.
• [12] Taghizadeh, N., Mirzazadeh, M., ‘‘Exact Travelling Wave Solutions for Konopelchenko-Dubrovsky Equation by the First Integral Method.’’ Appl. Appl. Math. 6 (2011): 153-161.
• [13] Cao, B., ‘‘Solutions of Jimbo-Miwa Equation and Konopelchenko-Dubrovsky Equations.’’ Acta Appl Math 112.2 (2010): 181-203.
• [14] Wazwaz, A., ‘‘New kinks and solitons solutions to the (2 + 1)-dimensional Konopelchenko–Dubrovsky equation.’’ Math. Comput. Model. 45.3-4 (2007): 473-479.
• [15] Song, L, Zhang, H., ‘‘New exact solutions for the Konopelchenko–Dubrovsky equation using an extended Riccati equation rational expansion method and symbolic computation.’’ Appl. Math. Comput. 187.2 (2007): 1373-1388.
• [16] Liu, Y, Yan, L., ‘‘Solutions of Fractional Konopelchenko-Dubrovsky and Nizhnik-Novikov-Veselov Equations Using a Generalized Fractional Subequation Method.’’ Abstr. Appl. Anal. 2013 (2013): 1-7.
• [17] Zheng, B, Qinghua, F., ‘‘The Jacobi Elliptic Equation Method for Solving Fractional Partial Differential Equations.’’ Abstr. Appl. Anal. 2014 (2014): 1- 9.
• [18] Mohyud-Din, S. T., Saba, F.,. ‘‘Extended -Expansion Method for Konopelchenko–Dubrovsky (KD) Equation of Fractional Order.’’ Int. J. Appl. Comput. Math 3 (2017): 161-172.
• [19] Liu, H-Z, Zhang, T., ‘‘A note on the improved -expansion method.’’ Optik 131 (2017): 273-278.
• [20] Manafian, J., Foroutan, M., ‘‘Application of -expansion method for the time-fractional Kuramoto–Sivashinsky equation.’’ Opt. Quant. Electron. 49.8 (2017): 272.
• [21] Manafian, J., Lakestani, M., ‘‘Optical soliton solutions for the Gerdjikov–Ivanov model via -expansion method.’’ Optik 127.20 (2016): 9603-9620.
• [22] Manafian, J., Lakestani, M., ‘‘Application of -expansion method for solving the Biswas–Milovic equation for Kerr law nonlinearity.’’ Optik 127.4 (2016): 2040-2054.
• [23] Hosseini, K., et al. ‘‘Resonant optical solitons with perturbation terms andfractional temporal evolution using improved -expansion method and exp function approach.’’ Optik 158 (2018): 933-939.
• [24] Khalil, R., et al. ‘‘A new definition of fractional derivative.’’ J. Comput. Appl. Math. 264 (2014): 65-70.