  In this paper we obtain new estimates of the Hadamard fractional derivatives
of a function at its extreme points. The extremum principle is then applied to
show that the initial-boundary-value problem for linear and nonlinear
time-fractional diffusion equations possesses at most one classical solution
and this solution depends continuously on the initial and boundary conditions.
The extremum principle for an elliptic equation with a fractional Hadamard
derivative is also proved.
