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arXiv · 1405.2813

A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration

Nadia Benkhettou·Artur M. C. Brito da Cruz·Delfim F. M. Torres
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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.

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Nadia Benkhettou, Artur M. C. Brito da Cruz, Delfim F. M. Torres. 2014-05-12. A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration. https://doi.org/10.1016/j.sigpro.2014.05.026

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