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Read or Download 41st IEEE Conference on Decision and Control, Tutorial Workshop No. 2: Fractional Calculus Applications in Automatic Control and Robotics (Las Vegas, USA, December 9, 2002): Lecture Notes PDF

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Additional info for 41st IEEE Conference on Decision and Control, Tutorial Workshop No. 2: Fractional Calculus Applications in Automatic Control and Robotics (Las Vegas, USA, December 9, 2002): Lecture Notes

Example text

To this integral, with the term (-1)p omitted, we give the name of Liouville fractional integral. In other papers, Liouville went ahead with the development of ideas concerning this theme, having presented a generalisation of the notion of incremental ratio to define a fractional derivative. This idea was recovered, later, by Grünwald (1867) and Letnikov (1868). 1) for the fractional integral. Holmgren (1865/66) and Letnikov (1868/74) discussed that problem when looking for the solution of differential equations, putting in a correct statement the fractional differentiation as inverse operation of the fractional integration.

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Of course, in applications to the study of causal systems, we must use the approach based on LT. 2. Differintegration of periodic functions Now, we are going to face the problem of the differintegration of a periodic function, xp(t). These functions do not have LT, but they have FT. A given periodic function, with period T, can be considered as a sum of delayed versions of a given basic wavelet. 14) that shows that the differintegrated of a periodic function can be obtained by convolving the wavelet with the differintegrated of the comb signal.

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