A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration
arXiv:1405.2813 · doi:10.1016/j.sigpro.2014.05.026
Abstract
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.
This is a preprint of a paper whose final and definite form will appear in the international journal Signal Processing, ISSN 0165-1684. Paper submitted 04/Jan/2014; revised 19/Apr/2014; accepted for publication 12/May/2014
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