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Title: A fractional calculus on arbitrary time scales: fractional differentiation and fractional integration
Author: Benkhettou, N.
Brito da Cruz, A. M. C.
Torres, D. F. M.
Keywords: Calculus on time scales
Fractional differentiation
Fractional integration
Time measurement
Arbitrary time
Fractional calculus
Local approaches
Order of differentiation
Real number
Differentiation (calculus)
Issue Date: Feb-2015
Publisher: Elsevier
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.
Peer review: yes
DOI: 10.1016/j.sigpro.2014.05.026
ISSN: 0165-1684
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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