  In this paper we present a new type of fractional operator, which is a
generalization of the Caputo and Caputo--Hadamard fractional derivative
operators. We study some properties of the operator, namely we prove that it is
the inverse operation of a generalized fractional integral. A relation between
this operator and a Riemann--Liouville type is established. We end with a
fractional Gronwall inequality type, which is useful to compare solutions of
fractional differential equations.
