Abstract: Using upper and lower solution method, we studied the existence of solution of fractionalorder periodic boundary value problem
x^(δ)(t)=f(t,x(t)),t∈［a,a+T］,a>0,
x(a)=x(a+T),
where f is a continuous function, f(a+T,x)=f(a,x), a>0, T>0 are constants and δ∈(0,1］. 

Key words: existence of solution, upper and lower solution method, periodic boundary value problem, fractionalorder