Results 21 to 30 of about 58,651 (306)
Fractional Dynamics at Multiple Times [PDF]
Journal of Statistical Physics, 2012 A continuous time random walk (CTRW) imposes a random waiting time between random particle jumps. CTRW limit densities solve a fractional Fokker-Planck equation, but since the CTRW limit is not Markovian, this is not sufficient to characterize the process.
Meerschaert, Mark M., Straka, Peter
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Rough Homogenisation with Fractional Dynamics [PDF]
, 2021 We review recent developments of slow/fast stochastic differential equations, and also present a new result on Diffusion Homogenisation Theory with fractional and non-strong-mixing noise and providing new examples. The emphasise of the review will be on the recently developed effective dynamic theory for two scale random systems with fractional noise ...
Gehringer, J, Li, X-M
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Dynamical Fractional and Multifractal Fields [PDF]
Journal of Statistical Physics, 2021 Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To reproduce the fractional, and more specifically multifractal, regularity nature of fully developed turbulence, these ...
Apolinario, Gabriel Brito +2 more
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Fractional Dynamics in Soccer Leagues [PDF]
Symmetry, 2020 This paper addresses the dynamics of four European soccer teams over the season 2018–2019. The modeling perspective adopts the concepts of fractional calculus and power law. The proposed model embeds implicitly details such as the behavior of players and coaches, strategical and tactical maneuvers during the matches, errors of referees and a multitude ...
António M. Lopes 0001 +1 more
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A class of CTRWs: Compound fractional poisson processes [PDF]
, 2011 This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. It begins with the characterization of a well-known Lévy process: The compound Poisson process.
Enrico Scalas +4 more
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Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models
Mathematics, 2019 This article is a review of problems and difficulties arising in the construction of fractional-dynamic analogs of standard models by using fractional calculus.
Vasily E. Tarasov
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Mathematics, 2020 In this paper, we consider a nonlinear fractional differential equation. This equation takes the form of the Bernoulli differential equation, where we use the Caputo fractional derivative of non-integer order instead of the first-order derivative.
Vasily E. Tarasov
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On History of Mathematical Economics: Application of Fractional Calculus
Mathematics, 2019 Modern economics was born in the Marginal revolution and the Keynesian revolution. These revolutions led to the emergence of fundamental concepts and methods in economic theory, which allow the use of differential and integral calculus to describe ...
Vasily E. Tarasov
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Integral Equations of Non-Integer Orders and Discrete Maps with Memory
Mathematics, 2021 In this paper, we use integral equations of non-integer orders to derive discrete maps with memory. Note that discrete maps with memory were not previously derived from fractional integral equations of non-integer orders.
Vasily E. Tarasov
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Analysis of Fractional Dynamic Systems [PDF]
The Scientific World Journal, 2014 Due to the extensive applications of fractional differential equations (FDEs) in engineering and science, research in this area has grown significantly. Fractional Dynamic Systems are described by FDEs, and this special issue consists of 8 original articles covering various aspects of FDEs and their applications written by prominent researchers in the ...
Fawang Liu +4 more
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