title: Integrodifferential diffusion equation for continuous-time random walk.
abstract: In this paper, we present an integrodifferential diffusion equation for continuous-time random walk that is valid for a generic waiting time probability density function. Using this equation, we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential and a combination of power law and generalized Mittag-Leffler function. We show that for the case of the exponential waiting time probability density function, a normal diffusion is generated and the probability density function is Gaussian distribution. In the case of the combination of a power law and generalized Mittag-Leffler waiting probability density function, we obtain the subdiffusive behavior for all the time regions from small to large times and probability density function is non-Gaussian distribution.
authors.affiliation: Departamento de Física, Universidade Estadual de Maringá, 87020-900 Maringá, PR, Brazil. kwok@dfi.uem.br
authors.forename: Kwok Sau
authors.initials: KS
authors.lastname: Fa
authors.forename: K G
authors.initials: KG
authors.lastname: Wang