Eur. Phys. J. Plus (2017) 132: 92
https://doi.org/10.1140/epjp/i2017-11370-7

Regular Article

Tanh-type and sech-type solitons for some space-time fractional PDE models

¹ Çankırı Karatekin University, Department of International Trade, 18200, Çankırı, Turkey
² Eskişehir Osmangazi University, Department of Mathematics & Computer, 26200, Eskişehir, Turkey
³ Çankırı Karatekin University, Department of Mathematics, 18200, Çankırı, Turkey

^* e-mail: ozkanguner@karatekin.edu.tr

Received: 5 December 2016
Accepted: 23 January 2017
Published online: 22 February 2017

Abstract

Tanh-type and sech-type soliton solutions are constructed for the fractional modified KdV-Zakharov-Kuznetsov equation and the fractional generalized Duffing equation. Both equations are reduced to ordinary differential equations by using compatible fractional complex transforms. Suitable powers of tanh and sech ansatzs including unknown free parameters are applied to both equations. After determining the powers, these parameters are determined using computer algebra. The obtained soliton solutions are depicted for particular cases for various values of derivative order.