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Topic: Differintegral

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	Differintegral
		In mathematics, the combined differentiation/integration operator used in fractional calculus is called the differintegral, and it has a few different forms which are all equivalent.
		The RL differintegral is thus defined as(the constant is brought to the front):
		We therefore define the differintegral via its behavior in certain transformed spaces corresponding to some common transformations.
	www.ebroadcast.com.au /lookup/encyclopedia/di/Differintegral.html (393 words)

	Kids.Net.Au - Encyclopedia > Differintegral (Site not responding. Last check: 2007-10-16)
		When we are taking the differintegral at the upper bound (t), it is usually written:
		The most important difference is that its upper bound is infinity.
		Note, however, that there are no bounds of differintegration.
	www.kids.net.au /encyclopedia-wiki/di/Differintegral?title=Counting (420 words)

	Reference.com/Encyclopedia/Fractional order integrator
		The differintegral parameter q may be any real number or complex number.
		The integer order integration can be computed as a Riemann-Liouville differintegral, where the weight of each element in the sum is the constant unit value 1, which is equivalent to the Riemann sum.
		To compute an integer order derivative, the weights in the summation would be zero, with the exception of the most recent data points, where (in the case of the first unit derivative) the weight of the data point at t−1 is −1 and the weight of the data point at t is 1.
	www.reference.com /browse/wiki/Fractional_order_integrator (508 words)

	Initialized fractional calculus
		A certain oddity about the differintegral should be pointed out.
		This is exactly the problem that we encountered with the differintegral.
		If the differintegral is initialized properly, then the composition holds.
	www.ebroadcast.com.au /lookup/encyclopedia/in/Initialized_fractional_calculus.html (181 words)

	Differintegral - Wikipedia, the free encyclopedia
		In mathematics, the differintegral is the combined differentiation/integration operator used in fractional calculus.
		The operator does not define a separate function, but is a notation style for taking both the fractional derivative and the fractional integral of the same expression.
		This is formally similar to the Riemann-Liouville differintegral, but applies to periodic functions, with integral zero over a period.
	en.wikipedia.org /wiki/Differintegral (329 words)

	Initialized Fractional Calculus
		What enables the elimination of this requirement is the revision of definitions of integrals and derivatives of arbitrary orders to include initialization functions that carry the history of the differintegral.
		The initialization functions are generalizations of the constants of integration that appear in the ordinary calculus, where they are used to represent initial conditions.
		The concept of a variable-structure or variable-order differintegral was introduced.
	www.nasatech.com /Briefs/Oct02/LEW17139.html (586 words)

	Fractional calculus - Wikipedia, the free encyclopedia
		This property is called the Semi-Group property of fractional differintegral operators.
		The theory for periodic functions, therefore including the 'boundary condition' of repeating after a period, is the Weyl differintegral.
		It is defined on Fourier series, and requires the constant Fourier coefficient to vanish (so, applies to functions on the unit circle integrating to 0).
	en.wikipedia.org /wiki/Half-derivative (983 words)

	The Differintegral Model for Describing Fractal Coupling Between Waveguide Surfaces - Begell House Inc.
		The Differintegral Model for Describing Fractal Coupling Between Waveguide Surfaces - Begell House Inc.
		It was ascertained that the energy dissipation recording on a rectangular grating edge can well be made possible.
		The calculated characteristics of a differintegral model of the system are in good agreement with the findings of experimental investigations.
	www.begellhouse.com /journals/0632a9d54950b268,602dd49c2bcc592d,5b54af884ff7cbf9.html (106 words)

	UC Davis: Computational Science and Engineering : Variable Order Modeling and the Measure of Complexity in ...
		Variable-Order (VO) modeling of dynamical systems is an emerging area of research that involves the use of VO differential operators.
		In such operators, the order of differentiation q(x(t), t) (or integration if q < 0) of the differintegral equation representing the dynamical problem is a function of either the dependent or independent variables in the problem, or even an external function representing a given behavior.
		In this seminar, I will discuss some of the important characteristics of several VO operators that are based on generalization of the Caputo, Riemann-Liouville and Grünwald-Letnikov fractional derivatives, and we identify a VO operator that is suitable to the study of dynamical systems.
	cse.ucdavis.edu /public/events/variable-order-modeling-and-the-measure-of-complexity-in-convective-diffusive-flows (347 words)

	Fractional Calculus - Grunwald-Letnikov Derivative
		Grunwald-Letnikov derivative or also named Grunwald-Letnikov differintegral, is a generalization of the derivative analogous to our generalization by the binomial formula (4.6), but it is based on the direct generalization of the equation (1.4).
		The idea behind is that h should approach 0 as n approaches infinity,
		In the case of the derivative generalized by the binomial formula (4.6), since n goes to infinity regardless of h, x-a must be infinity, so that the derivative defined in (4.4) and (4.6) is equivalent to the Grunwald-Letnikov derivative with a lower limit of negative infinity.
	www.xuru.org /fc/GrunwaldLetnikov.asp (240 words)

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