Functional Variable Method for conformable fractional modified KdV-ZK equation and Maccari system

Abstract

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.

Traveling wave solutions for complex nonlinear space–time fractional order (2 + 1)-dimensional Maccari dynamical system and Schrödinger equation with dual power law nonlinearity

“…ESEM has been successfully used to extract different solutions for the space-time fractional (2 + 1)-dimensional 44) and (46) are siloton solutions. The solutions we found for the Maccari system are novel compared to integer order solutions that have been extracted in the literature [38][39][40][41].…”

General solution of second order fractional differential equations

“…Due to this fact, finding an approximate solution of fractional differential equations is clearly an important task. In recent years, many effective methods have been proposed for the approximate solution fractional differential equations, such as Adomian decomposition method [3,4], homotopy perturbation method [5][6][7][8], homotopy analysis method [9,10], variational iteration method [11], generalized differential transform method [12] and other methods [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. The organization of the paper is as follows: In Section 2, Basic definitions, such as conformable fractional derivative, and conformable fractional integral, will be presented.…”

New Travelling Wave Solutions for Time-Space Fractional Liouville and Sine-Gordon Equations

“…Also, Caputo definition is limited because it is assumed that the function must be differentiable (Cenesiz et al, 2017).…”