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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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ON HADAMARD FRACTIONAL CALCULUS
Fractals, 2017This paper is devoted to the investigation of the Hadamard fractional calculus in three aspects. First, we study the semigroup and reciprocal properties of the Hadamard-type fractional operators. Then, the definite conditions of certain class of Hadamard-type fractional differential equations (HTFDEs) are proposed through the Banach contraction ...
Li Ma, Changpin Li
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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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Introduction to Fractional Calculus
2021Fractional calculus is the basis of the fractional-order circuit, which was born almost simultaneously as the classical integer-order calculus.
Bo Zhang, Xujian Shu
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Lattice fractional calculus [PDF]
Applied Mathematics and Computation, 2015 Integration and differentiation of non-integer orders for N-dimensional physical lattices with long-range particle interactions are suggested. The proposed lattice fractional derivatives and integrals are represented by kernels of lattice long-range interactions, such that their Fourier series transformations have a power-law form with respect to ...
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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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Fractional Calculus in Bioengineering, Part3
Critical Reviews in Biomedical Engineering, 2004Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the ...
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Essentials of Fractional Calculus
2017In recent decades, the field of fractional calculus has attracted interest of researchers in several areas including mathematics, physics, chemistry, engineering, and even finance and social sciences.
Hans J. Haubold, Arak M. Mathai
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Chaos, Solitons & Fractals, 2009
Abstract Here are presented fractional Taylor type formulae with fractional integral remainder and fractional differential formulae, regarding the right Caputo fractional derivative, the right generalized fractional derivative of Canavati type [Canavati JA. The Riemann–Liouville integral.
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Abstract Here are presented fractional Taylor type formulae with fractional integral remainder and fractional differential formulae, regarding the right Caputo fractional derivative, the right generalized fractional derivative of Canavati type [Canavati JA. The Riemann–Liouville integral.
openaire +2 more sources