分布序演算与超低速扩散方程
Distributed Order Calculus and Equations of Ultraslow Diffusion
摘要：
考虑了时间变量具有分布阶导数的扩散型方程.该导数被定义为具有某个正权函数的$α\in (0,1)$阶Caputo-Dzhrbashian分数阶导数在$α$中的积分。这种方程在物理文献中用于模拟具有均方位移的对数增长的扩散。本文建立了这类方程的数学理论，研究了分布阶导数和分布阶积分。
英文摘要：
We consider diffusion type equations with a distributed order derivative in the time variable. This derivative is defined as the integral in $α$ of the Caputo-Dzhrbashian fractional derivative of order $α\in (0,1)$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
