  We consider Hadamard fractional derivatives and integrals of variable
fractional order. A new type of fractional operator, which we call the
Hadamard-Marchaud fractional derivative, is also considered. The objective is
to represent these operators as series of terms involving integer-order
derivatives only, and then approximate the fractional operators by a finite
sum. An upper bound formula for the error is provided. We exemplify our method
by applying the proposed numerical procedure to the solution of a fractional
differential equation and a fractional variational problem with dependence on
the Hadamard-Marchaud fractional derivative.
