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Title: Nonlinear Time-Fractional Differential Equations in Combustion Science
Authors: Pagnini, Gianni
Keywords: Time-Fractional Derivative
Nonlinear Equation
Anomalous Diffusion
Combustion Science
Premixed Flame Ball
Issue Date: 2011
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 14, No 1, (2011), 80p-93p
Abstract: The 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.
Description: MSC 2010: 34A08 (main), 34G20, 80A25
ISSN: 1311-0454
Appears in Collections:2011

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