This paper aims as the stability and large-time behavior of 3D incompressible Magnetohydrodynamic (MHD) equations with fractional horizontal dissipation and magnetic diffusion. By using the energy methods , we obtain that if the initial data is small enough in H3 (R3), then this system possesses a global solution, and whose horizontal derivatives decay at least at the rate of (1 + t) − 1/2 . Moreover, if we control the initial data further small in H3(R3) ∩ Hh −1 (R3), the sharp decay of this solution and its first-order derivatives are established.
Mathematics Subject Classification. 35Q35, 35B35, 35B40, 76D03.