Mohammed O. AL-AMR, University of Mosul, Iraq

In this paper, based on the definition of conformable fractional derivative, the functional variable method (FVM) is proposed to seek the exact traveling wave solutions of two higher-dimensional space-time fractional KdV-type equations in mathematical physics, namely the (3+1)-dimensional space–time fractional Zakharov-Kuznetsov (ZK) equation and the (2+1)-dimensional space–time fractional Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony (GZK-BBM) equation. Some new solutions are procured and depicted. These solutions, which contain kink-shaped, singular kink, bell-shaped soliton, singular soliton and periodic wave solutions, have many potential applications in mathematical physics and engineering. The simplicity and reliability of the proposed method is verified.

Functional Variable Method, Fractional Partial Differential Equations, Exact Solutions, Conformable Fractional Derivative