Nonlinear time-fractional differential equations in combustion science

Abstract

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 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.