Results 1 to 10 of about 13,293 (292)
TEMPERED FRACTIONAL CALCULUS. [PDF]
J Comput Phys, 2015 Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an ...
Meerschaert MM, Sabzikar F, Chen J.
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General Fractional Vector Calculus
Mathematics, 2021 A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators.
Vasily E. Tarasov
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Weighted Fractional Calculus: A General Class of Operators
Fractal and Fractional, 2022 We conduct a formal study of a particular class of fractional operators, namely weighted fractional calculus, and its extension to the more general class known as weighted fractional calculus with respect to functions.
Arran Fernandez, Hafiz Muhammad Fahad
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General Fractional Calculus: Multi-Kernel Approach
Mathematics, 2021 For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in 2021. In Luchko works, the proposed approaches to formulate this calculus are based either on the power of one Sonin kernel or the convolution of one ...
Vasily E. Tarasov
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A numerical framework for fractional and fractal-fractional analysis of the Pehlivan chaotic system using Caputo derivative [PDF]
Scientific ReportsThe Pehlivan chaotic system, introduced by Ibrahim Pehlivan and Yilmaz Uyaroglu, is a three-dimensional autonomous chaotic model with rich dynamical properties.
R. Vinoth, M. Jayalakshmi
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General Fractional Calculus in Multi-Dimensional Space: Riesz Form
Mathematics, 2023 An extension of the general fractional calculus (GFC) is proposed as a generalization of the Riesz fractional calculus, which was suggested by Marsel Riesz in 1949.
Vasily E. Tarasov
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Fractional calculus in pharmacokinetics [PDF]
Journal of Pharmacokinetics and Pharmacodynamics, 2017 We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics." The presence of fractional kinetics has important clinical implications such as the lack of a half-life, observed, for example with the ...
Pantelis Sopasakis +3 more
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On Weyl fractional calculus [PDF]
Proceedings of the American Mathematical Society, 1979 The Weyl fractional calculus is applied in developing the Laplace transform of t q
Raina, R. K., Koul, C. L.
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Complexity and the Fractional Calculus [PDF]
Advances in Mathematical Physics, 2013 We study complex processes whose evolution in time rests on the occurrence of a large and random number of events. The mean time interval between two consecutive critical events is infinite, thereby violating the ergodic condition and activating at the same time a stochastic central limit theorem that supports the hypothesis that the Mittag-Leffler ...
Pramukkul, Pensri +4 more
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Fuzzy clustering to classify several regression models with fractional Brownian motion errors
Alexandria Engineering Journal, 2020 Clustering regression models fitted on the dataset is one of the most ubiquitous issues in different fields of sciences. In this research, fuzzy clustering method is used to cluster regression models with fractional Brownian motion errors that can be ...
Mohammad Reza Mahmoudi +2 more
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