The asymptotics of the solutions to the anomalous diffusion equations

Authors:
Yutian Ma;Fengrong Zhang;Changpin Li
Affiliations:
Department of Mathematics, Shanghai University, Shanghai 200444, PR China and Department of Mathematics, Fuyang Teachers College, Fuyang 236037, PR China;China University of Petroleum (East China), Qingdao 266555, PR China;Department of Mathematics, Shanghai University, Shanghai 200444, PR China
Venue:
Computers & Mathematics with Applications
Year:
2013

Citing 3
Cited 0

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Abstract

In this paper, we study the asymptotics of the solutions to the anomalous diffusion equations. The fractional anomalous diffusion equations are obtained from the existing anomalous diffusion and typical diffusion equations by replacing the first-order time derivative with fractional derivatives of order @a@?(0,1) for the sub-diffusion and @a@?(1,2) for the super-diffusion respectively. In most situations, fractional derivatives mean Riemann-Liouville derivative or Caputo derivative. In this paper, we use these two kinds of fractional derivatives. Using Laplace transform and Fourier transform, we obtain the asymptotics estimates of solutions to the anomalous diffusion equations.