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For first time in my (loooong !) life, I heard, thanks to a question posted on SE, about fractional derivatives. In Wikipedia, I found very interesting material. But, being a physicist and not a real mathematician, could one explain me what they are used for ?

Thanks for your help

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    $\begingroup$ I think you should start with some tutorials you'll find on the internet... This could be a start:www3.nd.edu/~msen/Teaching/UnderRes/FracCalc.pdf $\endgroup$ – nullgeppetto Nov 19 '13 at 11:43
  • $\begingroup$ @geppeto. Thanks for the link. Now my life is still more difficult thanks to the fractional integrals ! $\endgroup$ – Claude Leibovici Nov 19 '13 at 11:56
  • $\begingroup$ :) You're welcome! $\endgroup$ – nullgeppetto Nov 19 '13 at 11:58
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It happens that I just see this old question. For such a long time, I suppose that you acquired as much useful information as expected.

A long time ago, I was interested on this subject. The book "The Fractional Calculus" from Keith B.Oldham, Jerome Spanier, Academic Press, New York, 1974 was of much greater use. Since that time, the number of publications is extensive.

I would mention this table, from https://fr.scribd.com/doc/14686539/The-Fractional-Derivation-La-derivation-fractionnaire , which shows a generalization of the basic electrotechnical components, thanks to the fractional differ-integration :

enter image description here

This is an interresting generalization especially in the field of impedance analysis. It makes understandable why the semi-circular complex impedance diagrams, with the center of circle depressed below the real axis, are so commonly observed in practice : https://fr.scribd.com/doc/71923015/The-Phasance-Concept

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  • $\begingroup$ Thank you very much ! This is a very interesting material, indeed ! Cheers :-) $\endgroup$ – Claude Leibovici Mar 28 '15 at 13:53

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