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Lattice fractional calculus [PDF]
Applied Mathematics and Computation, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Mathematical Gazette, 1936
1. Let f(x) be a real function of a real variable x. The meanings of when λ is a positive integer, a negative integer and zero, are well known. In the first case, denotes the λth integral of f(x) with respect to x, with an arbitrary lower limit of integration. In the second case, stands for the (−λ)th differential coefficient of f(x) with respect to
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1. Let f(x) be a real function of a real variable x. The meanings of when λ is a positive integer, a negative integer and zero, are well known. In the first case, denotes the λth integral of f(x) with respect to x, with an arbitrary lower limit of integration. In the second case, stands for the (−λ)th differential coefficient of f(x) with respect to
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The differentiability in the fractional calculus
Nonlinear Analysis, 2001Summary: In this work we give a general concept of differentiability of order \(\alpha\in]0,1]\) for functions of one variable, and then for functions of several variables, in the sense of Nishimoto's fractional calculus.
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Fractional Deterministic and Stochastic Calculus
2023Fractional calculus has emerged as a powerful and effective mathematical tool in the study of several phenomena in science and engineering. This text addressed to researchers, graduate students, and practitioners combines deterministic fractional calculus with the analysis of the fractional Brownian motion and its associated fractional stochastic ...
Ascione G., Mishura Y., Pirozzi E.
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Discretized Fractional Calculus
SIAM Journal on Mathematical Analysis, 1986Es werden für Fraktionalintegrale der Form \(\int^{x}_{0}(x- s)^{\alpha -1}x^{\beta -1}g(x)ds\) Konvolutionsquadraturen untersucht, d.h. numerische Näherungen in den Punkten \(x=0,h,2h,...Nh\) bestimmt. Es wird gezeigt, daß die angegebenen Methoden konvergent von der Ordnung p sind, wenn sie stabil und von der Ordnung p konsistent sind.
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2017
: Since the early 1960s, there have been a good number of papers related to heavy tail distributions. These papers support the view that the heavy tail property is a stylized fact about financial time series. Stable distributions have infinite variance, a property which is not found in empirical samples where empirical variance does not grow with the ...
Frank J. Fabozzi +2 more
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: Since the early 1960s, there have been a good number of papers related to heavy tail distributions. These papers support the view that the heavy tail property is a stylized fact about financial time series. Stable distributions have infinite variance, a property which is not found in empirical samples where empirical variance does not grow with the ...
Frank J. Fabozzi +2 more
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Introduction to Fractional Calculus [PDF]
, 2007 Fractional calculus is three centuries old as the conventional calculus, but not very popular amongst science and or engineering community. The beauty of this subject is that fractional derivatives (and integrals) are not a local (or point) property (or quantity). Thereby this considers the history and non-local distributed effects.
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Essentials of Fractional Calculus
2015Essentials of fractional calculus are presented. Different kinds of integral and differential operators of fractional order are discussed. The notion of the Riemann-Liouville fractional integral is introduced as a natural generalization of the repeated integral written in a convolution type form.
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On fractional calculus and fractional multipoles in electromagnetism
IEEE Transactions on Antennas and Propagation, 1996Summary: In this paper, using the concept and tools of fractional calculus, we introduce a definition for `fractional-order' multipoles of electric-charge densities, and we show that as far as their scalar potential distributions are concerned, such fractional-order multipoles effectively behave as `intermediate' sources bridging the gap between the ...
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IFAC Proceedings Volumes, 2008
Nuclear magnetic resonance (NMR) is a physical phenomenon widely used to study complex materials. NMR is governed by the Bloch equation, a first order non-linear differential equation. Fractional order generalization of the Bloch equation provides an opportunity to extend its use to describe a wider range of experimental situations.
Richard L. Magin +2 more
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Nuclear magnetic resonance (NMR) is a physical phenomenon widely used to study complex materials. NMR is governed by the Bloch equation, a first order non-linear differential equation. Fractional order generalization of the Bloch equation provides an opportunity to extend its use to describe a wider range of experimental situations.
Richard L. Magin +2 more
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