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Topic: Fractional order differentiation

Related Topics

Fractional calculus

Cauchy integral formula

	Fractional order integrator - Wikipedia, the free encyclopedia
		The fractional integrator is useful in fractional order control where the history of the system under control is important to the control system output.
		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.
		An example fractional order integrator is a modification of the standard integrator circuit, where a capacitor is used as the feedback impedance on an opamp.
	en.wikipedia.org /wiki/Fractional_order_integrator (497 words)

	Fractional calculus - Wikipedia, the free encyclopedia
		Notice here that fraction is then a misnomer for the exponent, since it need not be rational, but the term fractional calculus has become traditional.
		As far as the existence of such a theory is concerned, the foundations of the subject were laid by Liouville in a paper from 1832.
		The fractional derivative of a function to order a is often now defined by means of the Fourier or Mellin integral transforms.
	en.wikipedia.org /wiki/Fractional_calculus (933 words)

	Fractional calculus Information - TextSheet.com (Site not responding. Last check: 2007-10-15)
		Fractional 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.
	internshipasia.sferahost.com /encyclopedia/f/fr/fractional_calculus.html (312 words)

	Sobolev space - Wikipedia, the free encyclopedia
		A considerably stronger notion of smoothness is that of differentiability (because functions that are differentiable are also continuous) and a yet stronger notion of smoothness is that the derivative also be continuous (these functions are said to be C
		Differentiable functions are important in many areas, and in particular for differential equations.
		In such problems, there is some data (such as today's weather, or the shape and water distribution of the food in the microwave oven) and there is a prediction (such as tomorrow's weather, or the time required to cook the food in the microwave.) In some cases, it is difficult to do an accurate simulation.
	en.wikipedia.org /wiki/Sobolev_space (1467 words)

	Applications of Fractional Calculus
		Fractional calculus concerns the generalization of differentiation and integration to non-integer (fractional) orders.
		Although fractional calculus is a natural generalization of calculus, and although its mathematical history is equally long, it has, until recently, played a negligible role in physics.
		Many applications of fractional calculus amount to replacing the time derivative in an evolution equation with a derivative of fractional order.
	www.ica1.uni-stuttgart.de /Jahresberichte/00/node50.html (259 words)

	Fractional calculus (Site not responding. Last check: 2007-10-15)
		As far as the existence of such a theory is concened, the foundations of the subject were laid by Liouville in a paper from 1832.
		The fractional derivative of a function to order a is often now defined by means of the Fourier transform.
		The classical form of fractional calculus is given by the Riemann-Liouville differintegral.
	www.sciencedaily.com /encyclopedia/fractional_calculus (581 words)

	Magmatic Differentiation
		If olivine fractionation were the process responsible for the change from magma A to magma B, then these proportions would have to be the same on all other variation diagrams as well.
		In order for crystal fractionation to operate their must be a natural mechanism that can remove crystals from the magma or at least separate the crystals so that they can no longer react with the liquid.
		In order to assimilate the country rock enough heat must be provided to first raise the country rock to its solidus temperature where it will begin to melt and then further heat must be added to change from the solid state to the liquid state.
	www.tulane.edu /~sanelson/eens211/magmadiff.htm (4859 words)

	Natural Order - Universal Relativity (Site not responding. Last check: 2007-10-15)
		The order of its differentiation is - n, where represents the order of the Universe in its entirety, and n the order of that holon on the integrarchic scale.
		The higher the order, the higher is the number of the groups of the variable components, and the greater is the complexity, stability and also the freedom and diversity of the holon.
		Differentiation, that is, evolution of new sub-types does not come about by random chance, but by intelligent self-design, where the more evolved type has the better means for further development: his brains.
	www.sesquiq.org /naturalorder.html (7783 words)

	Fractional Paradigm in Electrodynamics
		Engheta, "On Fractional Calculus and Fractional Multipoles in Electromagnetism,"
		We are interested in bringing the concept of fractional operators, fractional calculus and the theory of electrodynamics together, and to develop an area in electromagnetics which we have named
		We have applied the concept/tools of fractional calculus in certain problems in electromagnetic theory, and have obtained interesting results that demonstrate some salient physical features and mathematical properties of these operators with applications in radiation and scattering problems.
	www.ee.upenn.edu /~engheta/Fractional_Paradigm_in_EM.htm (314 words)

	[No title] (Site not responding. Last check: 2007-10-15)
		I was wondering whether any useful system has been worked out for >fractional-order differentiation, and what it has been or might be used >for.
		I mean a system where for example one can have not only first-order >and second-order differentials, but also one-and-a-halfth order >differentials etc. What with the use of fractional dimensionality in >chaos, ISTM that fractional-order differentials might also have a use >therein.
		The derivative of the integral of order k is the integral of order k-1 if k > 1.
	www.math.niu.edu /~rusin/known-math/01_incoming/fracder (174 words)

	Differentiation (from analysis) -- Encyclopædia Britannica (Site not responding. Last check: 2007-10-15)
		Differentiation is about rates of change; for geometric curves and figures this means determining the slope, or tangent, along a given direction.
		In contrast to the abstract nature of the theory behind it, the practical technique of differentiation can be carried out by purely algebraic manipulations, using three basic derivatives, four rules of operation, and a knowledge of how to manipulate functions.
		Its historical origins are in attempts to calculate such spatial quantities as the length of a curved line and the area enclosed by a curve.
	www.britannica.com /eb/article?tocId=218268 (873 words)

	Fractional Calculus (Site not responding. Last check: 2007-10-15)
		fractional calculus, fractional integral, fractional derivatives, fractional differential equations.
		It is a generalization of the ordinary differentiation and integration to non-integer (arbitrary) order.
		The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation.
	www.steveselectronics.com /petras/FC.html (342 words)

	Stefan Samko homepage - Research papers
		Fractional integrodifferentiation on the half-axis invariant with respect to dilatation (Russian) (with M.U.Yahshiboev).
		Multidimensional fractional differentiation which is invariant relative to dilatation, expressed in terms of fractional differences (with M.U.Yakhshiboev), Deponierted in VINITI, December 12, 1991, 4901-B91 DEP.
		Fractional Weyl-Riesz Integro-differentiation of periodic functions of two variables via the periodization of the Riesz kernel, Applicable Analysis, 2003, v.
	w3.ualg.pt /~ssamko/respapers (2447 words)

	Magmatic Differentiation
		As we might expect, elements that are excluded from crystals during fractionation should have their concentrations increase in the fractionated magmas.
		The concentration of incompatible trace elements should thus increase with increasing crystal fractionation, and the concentration of compatible trace elements should decrease with fractionation.
		Note that the REE patterns produced by higher percentages of crystal fractionation show higher concentrations, yet the patterns remain nearly parallel to one another.
	www.tulane.edu /~sanelson/geol212/magmadiff.htm (5554 words)

	Calculus I (Math 2413) - Derivatives - Higher Order Derivatives (Site not responding. Last check: 2007-10-15)
		Now, this is a function and so it can be differentiated. Here is the notation that we’ll use for that as well as the derivative.
		Okay, we know that in order to get the second derivative we need the first derivative and in order to get that we’ll need to do implicit differentiation. Here is the work for that.
		There is some alternate notation for higher order derivatives as well. Recall that there was a fractional notation for the first derivative.
	tutorial.math.lamar.edu /AllBrowsers/2413/HigherOrderDerivatives.asp (661 words)

	Fractional Differentiation V
		Thereby the order of differentiation reflects the local geometric structure of the processes.
		A stochastic version of this relation may be used for interpreting fractional Brownian motion of lower order by means of Weyl-Marchaud derivatives of fractional Brownian motion of higher order.
		The fractional degree of differentiability is introduced in section 4.
	www.minet.uni-jena.de /geometrie/publicat/htmfiles/fracdi5/fracdi5.htm (611 words)

	IL-12 is required for differentiation of pathogenic CD8+ T cell effectors that cause myocarditis -- Grabie et al. 111 ...
		IL-12 is required for differentiation of pathogenic CD8+ T cell effectors that cause myocarditis -- Grabie et al.
		The influence of IL-12 on activation and differentiation of OT-I cells in vitro.
		Phenotype of OT-I effector cells differentiated in vitro in the absence or presence of exogenous IL-12.
	www.jci.org /cgi/content/full/111/5/671 (5184 words)

	Amazon.co.uk: Books: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional ... (Site not responding. Last check: 2007-10-15)
		For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'.
		This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models.
		This work is a reference to fractional calculus for researchers and engineers needing applications tools for modelling, numerical methods, and plot visualization (2D and 3D).
	www.amazon.co.uk /exec/obidos/ASIN/0125588402 (542 words)

	Dr Chen, YangQuan's Fractional Order Control (FOC) Webpage
		The 2nd IFAC FDA06: Workshop on Fractional Differentiation and its Applications (Chair: Stefan Samko and co-Chair: Blas M. Vinagre)
		ASME First Symposium on Fractional Derivatives and Their Applications, International Design Engineering Technical Conferences, Chicago, Illinois September 2-6, 2003.
		Fractional calculus modeling of acoustic lossy media exhibiting arbitrary freqeuncy dependency and applications to medical ultrasonics.
	mechatronics.ece.usu.edu /foc (584 words)

	Fractional differential equations-Podlubny (Site not responding. Last check: 2007-10-15)
		[53] A. El-Sayed, On the fractional differential equations, Apll.
		[54] A. El-Sayed, Linear differential equations of fractional order, Apll.
		[55] A. El-Sayed, Multivalued fractional differential equations, Apll.
	myriam.ulpgc.es /711692.htm (4906 words)

	CANARIE Phase 3 (Site not responding. Last check: 2007-10-15)
		The implementation of portable Symbolic Web Server and its Mathematical Service Wrapper allows to install a new symbolic solving facility by a university professor or a developer of computer algebra package, because it assumes no special knowledge about the specifics of this architecture.
		For example, experts in symbolic computation, proficient in Maple, were able to develop a set of Maple packages solving specific problems such as Symbolic and Fractional Differentiation, Approximate GCD for polynomials and then used the Symbolic Web Server to create mathematical web services to make solvers for those problems available on the framework.
		Fractional order differentiation (developed as a MONET symbolic service).
	www.orcca.on.ca /MONET/docs/CA_Monet_final_report.html (2375 words)

	Enhanced Proliferation, Survival, and Dopaminergic Differentiation of CNS Precursors in Lowered Oxygen -- Studer et al. ...
		Ericson J, Muhr J, Placzek M, Lints T, Jessell TM, Edlund T (1995) Sonic hedgehog induces the differentiation of ventral forebrain neurons: a common signal for ventral patterning within the neural tube.
		Max SR, Bossio A, Iacovitti L (1996) Co-expression of tyrosine hydroxylase and glutamic acid decarboxylase in dopamine differentiation factor-treated striatal neurons in culture.
		Nurse CA, Vollmer C (1997) Role of basic FGF and oxygen in control of proliferation, survival, and neuronal differentiation in carotid body chromaffin cells.
	www.jneurosci.org /cgi/content/full/20/19/7377 (5473 words)

	VISUALIZATION OF FRACTIONAL CRYSTALLIZATION USING A SPREADSHEET PROGRAM (Site not responding. Last check: 2007-10-15)
		The concept of fractional crystallization as a mechanism of magmatic differentiation is typically introduced in physical geology courses and developed in more detail in petrology courses.
		It also enables the user to perform a series of fractional crystallization events (starting with a basaltic magma) to visualize how the residual magma changes in chemical composition as fractionation progresses.
		The utility of this approach in teaching fractional crystallization will be assessed more rigorously in a sophomore level course on earth materials.
	gsa.confex.com /gsa/2001NC/finalprogram/abstract_4401.htm (254 words)

	Differentiation of Viable and Nonviable Myocardium by the Use of Three-Dimensional Tagged MRI in 2-Day-Old Reperfused ... (Site not responding. Last check: 2007-10-15)
		Differentiation of Viable and Nonviable Myocardium by the Use of Three-Dimensional Tagged MRI in 2-Day-Old Reperfused Canine Infarcts -- Croisille et al.
		Differentiation of Viable and Nonviable Myocardium by the Use of Three-Dimensional Tagged MRI in 2-Day-Old Reperfused Canine Infarcts
		When coupled with a stress test, regional strain can be used to differentiate between viable but stunned and nonviable myocardium within the postischemic injured myocardium.
	circ.ahajournals.org /cgi/content/full/99/2/284 (5162 words)

	[No title]
		This is the topic of Fractional Order Derivatives (or Integrals), aka Fractional Calculus, and was studied by a bunch of mathematicians in early 1900s and late 1800s, including Riemann and a whole bunch of big names my brain's too dusty and rusty to recall.
		Even sticking with the gamma, it turns out that fractional order derivatives have a kind of looseness - the operator used in the electrochemistry paper, and seen elsewhere, is not the one you and I are playing with.
		I think the title was "The fractional Calculus", and I remember it had the style of Academic Press.
	www.math.niu.edu /~rusin/known-math/99/frac_der (1335 words)

	Fractional Splines
		The purpose of this presentation is to describe a recent family of basis functions—the fractional B-splines—which appear to be intimately connected to fractional calculus.
		Among other properties, we show that they are the convolution kernels that link the discrete (finite differences) and continuous (derivatives) fractional differentiation operators.
		This is in contrast with classical wavelets whose differentiation order is constrained to be an integer.
	bigwww.epfl.ch /publications/unser0403.html (315 words)

	Fractional Splines and Wavelets
		We extend Schoenberg's family of polynomial splines with uniform knots to all fractional degrees $\alpha>-1$.
		We show that these functions satisfy most of the properties of the traditional B-splines, including the convolution property, and a generalized fractional differentiation rule that involves finite differences only.
		Their most astonishing feature (in reference to the Strang--Fix theory) is that they have a fractional order of approximation $\alpha+1$ while they reproduce the polynomials of degree $\lceil\alpha\rceil$.
	epubs.siam.org /sam-bin/dbq/article/34943 (249 words)

	North American AC Fractional Horsepower Motor Markets - Market Research Report
		According to the research analyst, "Some manufacturers have undergone a number of consolidations and partnerships in order to reach a wider customer base and offer greater product selection." This is facilitating one-stop-shopping services for customers who want a single source of contact for fulfilling their needs.
		Focus on product differentiation, integrated systems packaging and higher quality customer service has enabled the motor manufacturers to gain and retain market share.
		Recent upturn in the economic conditions and increase in consumer spending are triggering the growth of major end-user industries of motors such as business equipment, domestic appliances, heat ventilating, and air conditioning machines.
	www.mindbranch.com /products/R1-2282.html (537 words)

	Fractional integration and constant Q
		By equation (61) and theorem 6, fractional powers of integration and differentiation are also impedance functions.
		Kjartansson [1979] has advocated the fractional power as a stress-strain law for rocks.
		Show the converse to theorem 4, namely, that if the phase curve of a causal function does not enclose the origin, then the inverse is causal.
	sepwww.stanford.edu /sep/prof/iei/crft/paper_html/node23.html (492 words)

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