Geodesic
Nonlinear Time-Fractional Differential Equations in Combustion Science
Fractional calculus and applied analysis, Tome 14 (2011) no. 1, pp. 80-93

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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.
Keywords: Time-Fractional Derivative, Nonlinear Equation, Anomalous Diffusion, Combustion Science, Premixed Flame Ball 
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     author = {Pagnini, Gianni},
     title = {Nonlinear {Time-Fractional} {Differential} {Equations} in {Combustion} {Science}},
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     publisher = {mathdoc},
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     number = {1},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/FCAA_2011_14_1_a4/}
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Pagnini, Gianni. Nonlinear Time-Fractional Differential Equations in Combustion Science. Fractional calculus and applied analysis, Tome 14 (2011) no. 1, pp. 80-93. http://geodesic.mathdoc.fr/item/FCAA_2011_14_1_a4/