By Blas M. Vinagre, YangQuan Chen (Eds.)

**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**

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Therefore, we will pursue a different way. Instead of beginning by a definition of differintegration, let us invert the problem and take the LT as the starting point, not only for the differentiation, but also for integration - differintegration. Essentially, we intend to prolong the sequence: ... , s ... 1) in order to include other kinds of exponents: rational or, generally, real (or even complex numbers). It is immediate to see that there are two forms of obtaining the extension, depending on the choice done for region of convergence for the LT: the left and right half-planes.

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.

### 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 by Blas M. Vinagre, YangQuan Chen (Eds.)

by Paul

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