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

**YANG Hui,WANG Wen-xia,WANG Jun-xia(Dept.of Mathematics,Taiyuan Normal University,Taiyuan 030012,China)**

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.

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