Anomalous diffusion and generalized diffusion equations

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. The forms of such equations might differ with respect to the position of the corresponding fractional operator in addition to or instead of the whole-number derivative in the Fick's equation. For processes lacking simple scaling the corresponding description may be given by distributed-order equations. In the present paper different forms of distributed-order diffusion equations are considered. The properties of their solutions are discussed for a simple special case.