Abstract
Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of application. This paper presents the analytical solutions of the space fractional diffusion equations by Adomian’s decomposition method (ADM). By using initial conditions, the explicit solutions of the equations have been presented in the closed form. Two examples, the first one is one-dimensional and the second one is two-dimensional fractional diffusion equation, are presented to show the application of the present techniques. The present method performs extremely well in terms of efficiency and simplicity.
Highlights
Fractional diffusion equations are used to model problems in Physics [1,2,3], Finance [4,5,6,7], and Hydrology [812]
Fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of application
This paper presents the analytical solutions of the space fractional diffusion equations by Adomian’s decomposition method (ADM)
Summary
Fractional diffusion equations are used to model problems in Physics [1,2,3], Finance [4,5,6,7], and Hydrology [812]. Fractional space derivatives may be used to formulate anomalous dispersion models, where a particle plume spreads at a rate that is different than the classical Brownian motion model. When a fractional derivative of order 1 < α < 2 replaces the second derivative in a diffusion or dispersion model, it leads to a super diffusive flow model. Consider a one-dimensional fractional diffusion equation considered in [17]
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