分数阶微分方程连续解的存在性定理

The Theorem of Existence of Continuous Solution for a Fractional Differential Equation

研究了更为一般的分数阶微分方程是否存在连续解的问题.若微分方程中的函数满足条件f(t,u)-f(t,v)≤λ(t)h(r)时,由于考虑到了该微分方程所等价的积分方程,故通过定义算子利用Schander不动点定理得到了此类分数阶微分方程连续解的存在性定理.当λ(t)为常数时,条件变为了Osgood条件,进而将经典的Osgood条件存在性定理推广到了一般的分数阶微分方程中.

The existence of continuous solutions of the more generalized fractional differential equations was studied.When the involved functions of differential equations satisfy the condition ｜f（t,u）-f（t,v）｜≤λ（t）h（r）, the differential equation is equivalent to the integral equation.By defining the operator and using Schander fixed point theorem,the continuous existence theorem was proved.When λ（t） is a constant,the condition becomes a Osgood condition,then the existence theorem of the classical Osgood conditions extends to more generalized fractional differential equations.