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 variational iteration method (VIM). 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 [8,9,10,11,12]
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 variational iteration method (VIM)
Summary
Fractional diffusion equations are used to model problems in Physics [1,2,3], Finance [4,5,6,7], and Hydrology [8,9,10,11,12]. We assume that the diffusion coefficient (or diffusivity) In physical applications, this means that the left/lower boundary is set far away enough from an evolving plume that no significant concentrations reach that boundary. The method has been proved by many authors [23,24,25,26], and the references therein, to be reliable and efficient for a wide variety of scientific applications, linear and nonlinear as well. We use the VIM to solve fractional diffusion Equations (1) and (2) and the results are illustrated in graphical figures
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