Solutions of fractional nonlinear diffusion equation and first passage time: Influence of initial condition and diffusion coefficient

Abstract

We investigate the solutions and the first passage time for anomalous diffusion processes governed by the fractional nonlinear diffusion equation with diffusion coefficient separable in time and space, D ( t , x ) = D ( t ) | x | − θ , subject to absorbing boundary condition and the conventional initial condition p ( x , 0 ) = δ ( x − x 0 ) . We obtain explicit analytical expressions for the probability distribution, the first passage time distribution, the mean first passage time and the mean squared displacement, and discuss their behavior corresponding to different time dependent diffusion coefficients.