．分数阶差分方程由于其数学模型的不断出现及

对微分方程近似计算的需要，也在近两年逐渐成为了学者关注的研究课题．本文主

要讨论了分数阶微分方程与分数阶泛函微分方程解的延拓理论、初值问题的解与

正解存在性与唯一性、边值问题正解的存在性；分数阶差分方程解的存在性与唯一

性、边值问题正解的存在性．-The study of fractional discrete equa—

tion have become a new reseazch topic in recent years．In this paper we mainly

discuss the fractional differential．equation theory，for example the continuation of

solutions for initial value problems，the existence and uniqueness of the solution

and boundary value problem positive solution．Also the existence and uniqueness

of solution of initial value problem and positive solution of boundary value problem

to fractional discrete equation