  It is well-known that if one replaces standard velocity and magnetic
dissipation by $(-\Delta)^\alpha u$ and $(-\Delta)^\beta b$ respectively, the
magnetohydrodynamic equations are well-posed for $\alpha\ge\frac{5}{4}$ and
$\alpha + \beta \ge \frac{5}{2}$. This paper considers the 3D Navier-Stokes and
magnetohydrodynamic equations with partial fractional hyper-dissipation. It is
proved that when each component of the velocity and magnetic field lacks
dissipation along some direction, the existence and conditional uniqueness of
the solution still hold. This paper extends the previous results in (Yang, Jiu
and Wu J. Differential Equations 266(1): 630-652, 2019) to a more general case.
