(4)Two effective approaches for solving fractional generalized Hirota-Satsuma coupled KdV system arising in interaction of long waves
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Ali Kurt a,∗, Hadi Rezazadeh b, Mehmet Senol c, Ahmad Neirameh d, Orkun Tasbozan a,
Mostafa Eslami e, Mohammad Mirzazadeh f
a Department of Mathematics, Mustafa Kemal University, Hatay, Turkey
b 2Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran
c Department of Mathematics, Nevsehir Haci Bektas Veli University, Nevsehir, Turkey
d Department of Mathematics, Faculty of Sciences, Gonbad Kavous University, Gonbad, Iran
e Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
f Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran
Received 13 November 2018; received in revised form 17 December 2018; accepted 18 December 2018
Available online 21 December 2018
Abstract
In this article, two different methods, namely sub-equation method and residual power series method, have been used to obtain new exact and approximate solutions of the generalized Hirota-Satsuma system of equations, which is a coupled KdV model. The fractional derivative is taken in the conformable sense. Each of the obtained exact solutions were checked by substituting them into the corresponding system with the help of Maple symbolic computation package. The results indicate that both methods are easy to implement, effective and reliable. They are therefore ready to apply for various partial fractional differential equations.
© 2018 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Keywords: Hirota-Satsuma coupled KdV system; Sub-equation method; Power series method; Conformable fractional derivative.