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 higherdimensional 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