Nonlinear Time-Fractional Differential Equations in Combustion Science
Fractional Calculus and Applied Analysis, Tome 14 (2011) no. 1, p. 80.

Voir la notice de l'article dans European Digital Mathematics Library

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.
Classification : 35R11, 34A08, 80A25
Mots-clés : Time-Fractional Derivative, Nonlinear Equation, Anomalous Diffusion, Combustion Science, Premixed Flame Ball, time-fractional derivative nonlinear equation, anomalous diffusion, premixed flame ball 
@article{FCAA_2011__14_1_219525,
     author = {Pagnini, Gianni},
     title = {Nonlinear {Time-Fractional} {Differential} {Equations} in {Combustion} {Science}},
     journal = {Fractional Calculus and Applied Analysis},
     pages = {80},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2011},
     zbl = {1273.34013},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/FCAA_2011__14_1_219525/}
}
TY  - JOUR
AU  - Pagnini, Gianni
TI  - Nonlinear Time-Fractional Differential Equations in Combustion Science
JO  - Fractional Calculus and Applied Analysis
PY  - 2011
SP  - 80
VL  - 14
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/FCAA_2011__14_1_219525/
LA  - en
ID  - FCAA_2011__14_1_219525
ER  - 
%0 Journal Article
%A Pagnini, Gianni
%T Nonlinear Time-Fractional Differential Equations in Combustion Science
%J Fractional Calculus and Applied Analysis
%D 2011
%P 80
%V 14
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/FCAA_2011__14_1_219525/
%G en
%F FCAA_2011__14_1_219525
Pagnini, Gianni. Nonlinear Time-Fractional Differential Equations in Combustion Science. Fractional Calculus and Applied Analysis, Tome 14 (2011) no. 1, p. 80. https://geodesic-test.mathdoc.fr/item/FCAA_2011__14_1_219525/