Nonlinear Time-Fractional Differential Equations in Combustion Science

Pagnini, Gianni. "Nonlinear Time-Fractional Differential Equations in Combustion Science." Fractional Calculus and Applied Analysis 14.1 (2011): 80-93. <http://eudml.org/doc/219525>.

@article{Pagnini2011,
abstract = {MSC 2010: 34A08 (main), 34G20, 80A25The application of Fractional Calculus in combustion science to model the evolution in time of the radius of an isolated premixed flame ball is highlighted. Literature equations for premixed flame ball radius are rederived by a new method that strongly simplifies previous ones. These equations are nonlinear time-fractional differential equations of order 1/2 with a Gaussian underlying diffusion process. Extending the analysis to self-similar anomalous diffusion processes with similarity parameter ν/2 > 0, the evolution equations emerge to be nonlinear time-fractional differential equations of order 1−ν/2 with a non-Gaussian underlying diffusion process.},
author = {Pagnini, Gianni},
journal = {Fractional Calculus and Applied Analysis},
keywords = {Time-Fractional Derivative; Nonlinear Equation; Anomalous Diffusion; Combustion Science; Premixed Flame Ball; time-fractional derivative nonlinear equation; anomalous diffusion; premixed flame ball},
language = {eng},
number = {1},
pages = {80-93},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Nonlinear Time-Fractional Differential Equations in Combustion Science},
url = {http://eudml.org/doc/219525},
volume = {14},
year = {2011},
}

TY - JOUR
AU - Pagnini, Gianni
TI - Nonlinear Time-Fractional Differential Equations in Combustion Science
JO - Fractional Calculus and Applied Analysis
PY - 2011
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 14
IS - 1
SP - 80
EP - 93
AB - MSC 2010: 34A08 (main), 34G20, 80A25The application of Fractional Calculus in combustion science to model the evolution in time of the radius of an isolated premixed flame ball is highlighted. Literature equations for premixed flame ball radius are rederived by a new method that strongly simplifies previous ones. These equations are nonlinear time-fractional differential equations of order 1/2 with a Gaussian underlying diffusion process. Extending the analysis to self-similar anomalous diffusion processes with similarity parameter ν/2 > 0, the evolution equations emerge to be nonlinear time-fractional differential equations of order 1−ν/2 with a non-Gaussian underlying diffusion process.
LA - eng
KW - Time-Fractional Derivative; Nonlinear Equation; Anomalous Diffusion; Combustion Science; Premixed Flame Ball; time-fractional derivative nonlinear equation; anomalous diffusion; premixed flame ball
UR - http://eudml.org/doc/219525
ER -