  We introduce a general notion of fractional (noninteger) derivative for
functions defined on arbitrary time scales. The basic tools for the time-scale
fractional calculus (fractional differentiation and fractional integration) are
then developed. As particular cases, one obtains the usual time-scale Hilger
derivative when the order of differentiation is one, and a local approach to
fractional calculus when the time scale is chosen to be the set of real
numbers.
