Fractal aspects in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mstyle mathvariant="normal"><mml:mi>O</mml:mi></mml:mstyle></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> enriched combustion

Souza, J.W.G.; Santos, Alex Álisson Bandeira; Guarieiro, Lílian Lefol Nani; Moret, Marcelo A.

doi:10.1016/j.physa.2015.04.021

Cited by 9 publications

(3 citation statements)

References 21 publications

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“…At the moment, there are not many papers in which this approach is used to describe combustion processes. However, existing experimental studies (see, for example [37]) indicate the legitimacy of this approach. One of the main difficulties in using equations in fractional derivatives is finding their solutions.…”

Section: Discussionmentioning

confidence: 99%

“…where q(x; α, β) is the density of a fractional-stable law (37). According to the properties of fractional-stable laws [51] in case of parameter values β = 1, α = 2, the density q(x; 2, 1) becomes the density of the normal law, and in case β = 1, the density q(x; α, 1) is the density of a stable law.…”

Section: The Equations Of Anomalous Diffusionmentioning

confidence: 99%

“…The authors of [35,36] point out that anomalous diffusion occurs during heat transfer in low-dimensional systems. In the paper [37] devoted to the study of thermal radiation during the combustion of natural gas and acetylene, it was found that the combustion process was of a subdiffusion nature.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical Method for Solving of the Anomalous Diffusion Equation Based on a Local Estimate of the Monte Carlo Method

et al. 2022

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This paper considers a method of stochastic solution to the anomalous diffusion equation with a fractional derivative with respect to both time and coordinates. To this end, the process of a random walk of a particle is considered, and a master equation describing the distribution of particles is obtained. It has been shown that in the asymptotics of large times, this process is described by the equation of anomalous diffusion, with a fractional derivative in both time and coordinates. The method has been proposed for local estimation of the solution to the anomalous diffusion equation based on the simulation of random walk trajectories of a particle. The advantage of the proposed method is the opportunity to estimate the solution directly at a given point. This excludes the systematic component of the error from the calculation results and allows constructing the solution as a smooth function of the coordinate.

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Section: Discussionmentioning

confidence: 99%

Section: The Equations Of Anomalous Diffusionmentioning

confidence: 99%