What is the fractional derivative of exp(-x) * (x^-1)?

[suku]

what is

d^0.5/(dx)^0.5 {exp(-x)* (x^-1)



tks for any help.

 

[Mark44]

what is

d^0.5/(dx)^0.5 {exp(-x)* (x^-1)
tks for any help.

AFAIK there is no such thing. Do you have a text that defines what this is, or are you just asking?

The only derivatives I have ever heard of in working with calculus for many years are the zero-th derivative (the function itself), the first derivative, the second derivative, and so on. No negative order or fractional order derivatives.

 

[Hurkyl]

What definition of fractional derivative are you using?

(If you just came up with the idea yourself, go use google to research "fractional derivative")

 

[JJacquelin]

A few references :

[1] Keith B.Oldham, Jerome Spanier, The Fractional Calculus, Academic Press,
New York, 1974.
[2] Joseph Liouville, Sur le calcul des différentielles à indices quelconques, J. Ecole Polytech., v.13, p.71, 1832.
[3] Bernhard Riemann, Versuch einer allgemeinen auffasung der integration und differentiation, 1847, Re-édit.: The Collected Works of Bernhard Riemann,
Ed. H. Weber, Dover, New York, 1953
[4] Augustin L. Cauchy, Œuvres complètes, 1823, cité par R. Courant, D. Hilbert, Methods of Mathematical Physics, Ed. J.Wiley & Sons, New York, 1962.
[5] Hermann Weyl, Bemerkungen zum begriff des differentialquotienten gebrocherer ordnung, Viertelschr. Naturforsh. Gesellsch., Zürich, v.62, p.296, 1917.
[6] Harry Bateman, Tables of Integral Transforms, Fractional Integrals, Chapt.XIII,
Ed. Mc.Graw-Hill, New-York, 1954.
[8] Jerome Spanier, Keith B.Oldham, An Atlas of Functions, Ed. Harper & Row,
New York, 1987.
[9] Milton Abramowitz, Irene A. Stegun, Handbook of Mathematical Functions, Ed. Dover Pub., New York, 1970.
[10] Jean Jacquelin, Use of Fractional Derivatives to express the properties of Energy Storage Phenomena in electrical networks, Laboratoires de Marcoussis, Route de Nozay, 91460, Marcoussis, 1982.
[11] Oliver Heaviside, Electromagnetic Theory, 1920, re-édit.: Dover Pub., New York, 1950.

From a paper entitled : "La dérivation fractionnaire" (a review for general public, French-style)
http://www.scribd.com/people/documents/10794575-jjacquelin

 

[HallsofIvy]

Yes, there is such a thing as "fractional derivatives"

wikipedia has a page on it:
http://en.wikipedia.org/wiki/Fractional_calculus

 

[Anonymous217]

If I remember correctly, I think Feynman was playing with this stuff (without knowing that it was already discovered) when he was still in high school. Just a small bit of trivia and absolutely not related to the purpose of the topic.

 

[Mark44]

Yes, there is such a thing as "fractional derivatives"

wikipedia has a page on it:
http://en.wikipedia.org/wiki/Fractional_calculus

Well, I learned something new today!

 

[suku]

AFAIK there is no such thing. Do you have a text that defines what this is, or are you just asking?

The only derivatives I have ever heard of in working with calculus for many years are the zero-th derivative (the function itself), the first derivative, the second derivative, and so on. No negative order or fractional order derivatives.

Actually this field is a new one.Again not so new, riemann, liouville worked with it. U can google search or get a book on it. It exists really.

 

[Anonymous217]

^You're a couple posts too late.