Anatoly N. Kochubei
Distributed Order Calculus and Equations of Ultraslow Diffusion
(87K, LaTeX-2e)

ABSTRACT.  We consider diffusion type equations with a distributed order 
derivative in the time variable. This derivative is defined as the integral 
in $\alpha$ of the Caputo-Dzhrbashian fractional derivative of order $\alpha 
\in (0,1)$ with a certain positive weight function. Such equations are used 
in physical literature for modeling 
diffusion with a logarithmic growth of the mean square 
displacement. In this work we develop a mathematical theory of 
such equations, study the derivatives and integrals of 
distributed order.