This note deals with Hadamard fractional differential equation of order 3 < α ≤ 4, subject to a mixed boundary conditions on [1, e]. The investigation made here involves Hadamard integral operator of a function with a construction of an appropriate Green's function. Using its properties as well as its maximum value, we will be able to get Hartman-Winter and Lyapunov-type inequalities for a class of Hadamard fractional differential equations. Finally, we will illustrate this result by giving an example.