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Fractional Calculus and Applied Analysis

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Nonlinear time-fractional differential equations in combustion science

1Research and Development in Sardinia, CRS4 Center for Advanced Studies, Polaris Bldg. 1, 09010, Pula (CA), Italy

© 2011 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citation Information: Fractional Calculus and Applied Analysis. Volume 14, Issue 1, Pages 80–93, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: 10.2478/s13540-011-0006-8, January 2011

Publication History

Published Online:


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 re-derived 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.

MSC: 34A08 (main); 34G20; 80A25

Keywords: time-fractional derivative; nonlinear equation; anomalous diffusion; combustion science; premixed flame ball

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