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Mathematical modeling of tuberculosis using Caputo fractional derivative: a comparative analysis with real data. [PDF]
Sci RepBhatter S +3 more
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Is it Curbing-spread of SARS-CoV-2 Variants by Considering Non-linear Predictive Control? [PDF]
Biomed Eng Comput BiolNajafi M +4 more
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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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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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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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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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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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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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