关于分数阶微分方程解的注记  

A Note on Fractional Differential Equations

作　　者：郑艳萍[1] 王文霞[1] 刘宇民[1] 

机构地区：[1]太原师范学院数学系,山西太原030012

出　　处：《中北大学学报（自然科学版）》2011年第1期67-70,共4页Journal of North University of China(Natural Science Edition)

摘　　要：利用泛函分析中的经典分析方法,探讨了非线性分数阶微分方程的初值问题,其中微分方程的阶数q为区间(2,3]的任意实数,导数形式为Riemann-Liouville型导数.给出了该方程与相应的Voletrra积分方程的等价性,并在此基础上建立了其解的局部存在性与解的唯一性的充分条件.The initial problem for nonlinear fractional differential equation with order q in（2,3] and Riemann-Liouville differentiation were investigated with classical method of functional analysis.The equivalence between the above equations and the Volterra integral equation was given.And the sufficient conditions for the local existence and uniqueness of solutions were derived.

关 键 词：Rimann-Liouville型导数 局部解 唯一性 

分 类 号：O175.6[理学—数学]