# Nonlinear Time-Fractional Differential Equations in Combustion Science

Fractional Calculus and Applied Analysis (2011)

- Volume: 14, Issue: 1, page 80-93
- ISSN: 1311-0454

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topPagnini, 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 -

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