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Delay Approximation of Fractional Integrals
Author(s) -
Machado J. A. Tenreiro
Publication year - 2013
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.583
Subject(s) - fractional calculus , operator (biology) , mathematics , function (biology) , perspective (graphical) , mittag leffler function , biochemistry , chemistry , geometry , repressor , evolutionary biology , biology , transcription factor , gene
This paper explores the calculation of fractional integrals by means of the time delay operator. The study starts by reviewing the memory properties of fractional operators and their relationship with time delay. Based on the time response of the Mittag‐Leffler function an approximation of fractional integrals consisting of time delayed samples is proposed. The tuning of the approximation is optimized by means of a genetic algorithm. The results demonstrate the feasibility of the new perspective and the limits of their application.