Modeling the motion and propagation characteristics of waves have importance in coastal, ocean and maritime engineering. Especially, waves are the major source of environmental actions on beaches or on man-made fixed or floating structures in most geographical areas. So Maccari system has great application in mentioned areas. The modified KdV is ion acoustic perturbations evolution model in a plasma with two negative ion components which have different temperatures. As for the KdV equation, the modified ZK (mZK) equation arises naturally as weakly two-dimensional variations of the mKdV equation. In this paper authors used functional variable method(FVM) for the first time to obtain exact travelling wave and soliton solutions of conformable fractional modified KdV-Zakharov-Kuznetsov(mKdv-ZK) equation and Maccari system. As a consequence, new solutions are obtained and it is seen that FVM is an valuable and efficient tool for solving nonlinear equations and systems where the derivatives defined by means of conformable fractional derivative.

Tbilisi Mathematical Journal, Vol. 10(1) (2017), pp. 117-125