The Generalization of Comparison Theorems of Fractional Differential Equations with Riemann-Liouville’s Derivative

By use of the equivalence between the fractional differential equations and the corresponding Volterra integral equations, the range of the orderαof the comparison theorem is extended fromα∈(0,1) to α∈(n－1,n)n∈Z+, so that the comparison theorem for any arbitrary fractional order differential equations is obtained and the application scope of this theorem is enlarged.