  We propose a new fractional derivative, the Hilfer-Katugampola fractional
derivative. Motivated by the Hilfer derivative this formulation interpolates
the well-known fractional derivatives of Hilfer, Hilfer-Hadamard,
Riemann-Liouville, Hadamard, Caputo, Caputo-Hadamard, Liouville, Weyl,
generalized and Caputo-type. As an application, we consider a nonlinear
fractional differential equation with an initial condition using this new
formulation. We show that this equation is equivalent to a Volterra integral
equation and demonstrate the existence and uniqueness of solution to the
nonlinear initial value problem.
