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.