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

**Read Online 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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**Extra 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**

K 41st IEEE CONFERENCE ON DECISION AND CONTROL 43 TUTORIAL WORKSHOP #2. 12) which can be considered as the arithmetic mean of causal and anti-causal differintegrations, if we extend their regions of convergence to include the imaginary axis. This is the known Rieman-Hilbert problem: to define a function on the boundary of the analyticity regions of two functions. FT[δ where Cr and Cl represent the right and left half complex planes. This gives immediately ∆(ω) = (jω)α. Before finishing these considerations, we must put the question of the application fields of the second approach.

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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. Hadamard proposed a method of fractional differentiation based on the differentiation of Taylor´s series associated with the function, Weyl (1917) defined a fractional integration suitable to periodic functions and Marchaud (1927) presented a new form of differentiation based on finite differences.