On a Caputo-type Fractional Derivative

In this work we present a new dierential operator of arbitrary order dened
by means of a Caputo-type modication of the generalized fractional derivative recently
proposed by Katugampola. The generalized fractional derivative, when adequate limits
are considered, recovers the Riemann-Liouville and the Hadamard derivatives of arbitrary
order. Our dierential operator recovers as limiting cases the arbitrary order derivatives
proposed by Caputo and by Caputo-Hadamard. Some properties are presented, as well
the relation between this dierential operator of arbitrary order and the Katugampola
generalized fractional operator. As an application we prove the fundamental theorem of
fractional calculus associated with our operator.