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.