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Differintegral information


In fractional calculus, an area of mathematical analysis, the differintegral is a combined differentiation/integration operator. Applied to a function ƒ, the q-differintegral of f, here denoted by

is the fractional derivative (if q > 0) or fractional integral (if q < 0). If q = 0, then the q-th differintegral of a function is the function itself. In the context of fractional integration and differentiation, there are several definitions of the differintegral.

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Differintegral

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mathematical analysis, the differintegral is a combined differentiation/integration operator. Applied to a function ƒ, the q-differintegral of f, here denoted...

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Initialized fractional calculus

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analysis, initialization of the differintegrals is a topic in fractional calculus. The composition law of the differintegral operator states that although:...

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Inverse Laplace transform

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analysis of the Inverse Laplace transform, using the Grunwald–Letnikov differintegral to evaluate the derivatives. Post's inversion has attracted interest...

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Weyl integral

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In mathematics, the Weyl integral (named after Hermann Weyl) is an operator defined, as an example of fractional calculus, on functions f on the unit circle...

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List of harmonic analysis topics

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kernel Gibbs phenomenon Parseval's identity Parseval's theorem Weyl differintegral Generalized Fourier series Orthogonal functions Orthogonal polynomials...

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Neopolarogram

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methods to implement a numerical calculation of fractional differintegrals. Yet differintegrals are faster to compute in discrete fourier space using FFT...

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Cauchy formula for repeated integration

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In fractional calculus, these formulae can be used to construct a differintegral, allowing one to differentiate or integrate a fractional number of times...

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Fractional calculus

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\end{aligned}}} This relationship is called the semigroup property of fractional differintegral operators. The classical form of fractional calculus is given by the...

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Autoregressive fractionally integrated moving average

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filter or similar. Fractional calculus — fractional differentiation Differintegral — fractional integration and differentiation Fractional Brownian motion...

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Generalizations of the derivative

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The −1 order derivative corresponds to the integral, whence the term differintegral. In quaternionic analysis, derivatives can be defined in a similar way...

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