- #1
suku
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what is
d^0.5/(dx)^0.5 {exp(-x)* (x^-1)
tks for any help.
d^0.5/(dx)^0.5 {exp(-x)* (x^-1)
tks for any help.
suku said:what is
d^0.5/(dx)^0.5 {exp(-x)* (x^-1)
tks for any help.
From a paper entitled : "La dérivation fractionnaire" (a review for general public, French-style)[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.
Well, I learned something new today!HallsofIvy said:Yes, there is such a thing as "fractional derivatives"
wikipedia has a page on it:
http://en.wikipedia.org/wiki/Fractional_calculus
Mark44 said: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.
A fractional derivative is a mathematical operation that generalizes the concept of a derivative to non-integer orders. It is a way to describe the rate of change of a function at a certain point, where the order of the derivative can be any real or complex number.
A fractional derivative is typically calculated using the Riemann-Liouville or Caputo definition. These methods involve taking the integral of the function to a certain power, and then evaluating it at a specific point. The order of the derivative determines the power used in the integral.
Fractional derivatives have various applications in physics, engineering, and other fields. They can be used to model systems with memory or non-local behavior, such as viscoelastic materials, electrical circuits, and diffusion processes. They also have applications in signal processing, image processing, and finance.
The main difference between a fractional derivative and a regular derivative is the order or degree of the derivative. A regular derivative has to be an integer, while a fractional derivative can be any real or complex number. Additionally, a fractional derivative takes into account the entire history of a function, while a regular derivative only considers the function at a specific point.
There are some limitations and challenges associated with fractional derivatives. One major challenge is the lack of a unified definition for fractional derivatives, as different definitions can lead to different results. Another limitation is the difficulty in interpreting the physical meaning of fractional derivatives, as they can describe non-local or non-physical behavior. Additionally, numerical methods for calculating fractional derivatives can be computationally expensive and may suffer from stability issues.