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Fractional_calculus (including recent related patents.)
Fractional calculusBack to: Mathematics | Next topic: DifferintegralsFractional calculus is a part of mathematics dealing with generalisations of the derivative to derivatives of arbitrary order (not necessarily an integer). The name "fractional calculus" is somewhat of a misnomer since the generalisations are by no means restricted to fractions, but the label persists for historical reasons. The fractional derivative of a function to order a is often defined implicitly by the Fourier transform. The fractional derivative in a point x is a local property only when a is an integer. Applications of the fractional calculus includes partial differential equations, especially parabolic ones where it is sometimes useful to split a time-derivative into fractional time. There are many well known fields of application where we can use the fractional calculus. Just a few of them are: Math-oriented Chaos theory Fractals Control theory Physics-oriented Electricity Mechanics Heat conduction Viscoelasticity Hydrogeology Nonlinear geophysics Table of contents showTocToggle("show","hide") 1 History 2 Differintegrals 3 Elementary topics 4 Forms of fractional calculus 5 Closely related topics 6 External Resources 6.1 External links 6.2 Resource Books History (fill this in (it started about 300 years ago.)) Differintegrals The combined differentation/integral operator used in fractional calculus is called the differintegral, and it has a couple of different forms which are all equivalent. (provided that they are initialized (used) properly.) By far, the most common form is the Riemann-Liouville form: definition(where Ψ(t) is a complementary function.) Elementary topics
This article is adapted from from Wikipedia All Wikipedia article text is available under the terms of the GNU Free Documentation License Physics of Fractal Operators by Bruce J. West The Fractional Calculus; Theory and Applications of Differentiation and Integration to Arbitrary Order (Mathematics in Science and Eng by Keith B. Oldham Recent Advances in Fractional Calculus (Global Research Notes in Mathematics Ser.) by R.N. Kalia Univalent Functions, Fractional Calculus, and Their Applications by H. M. Srivastava Fractional Differential Equations by Igor Podlubny Generalized Convexity and Fractional Program by Fractional Programmi International Workshop on "Generalized Concavity Fractional Calculus (Pitman Research Notes in Mathematics, No 138) by A. C. McBride Fractional Calculus and Integral Transforms of Generalized Functions (Research in Mathematics Series No 31) by Adam C. McBride Fractional Calculus: Integrations and Differentiations of Arbitrary Order by Katsuvuki Nishimoto Recent Advances in Fractional Calculus (Global Research Notes in Mathematics Ser.) by R.N. Kalia Fractals and Fractional Calculus in Continuum Mechanics (Cism International Centre for Mechanical Sciences, 378) by A. Carpinteri Generalized functions for the fractional calculus (SuDoc NAS 1.60:209424) by Carl F. Lorenzo Generalized Fractional Calculus and Applications by Virginia S. Kiryakova Univalent Functions, Fractional Calculus, and Their Applications (Ellis Horwood Series in Mathematics and Its Applications) by H.M. Srivastava Fractional Calculus and Its Applications: Proceedings of the International Conference Held at the University of New Haven, June, 1974 (Lecture Notes) by Bertram Ross Recent Fractional_calculus related patents From USPTO: |