含Riemann-Liouville导数分数阶微分方程比较定理的推广

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

摘要

摘要:利用分数阶微分方程与相应的Volterra积分方程的等价性,将含Riemann-Liouville导数的分数阶微分方程比较定理中的阶数α的取值范围由(0,1)推广到(n-1,n),n∈〖WTHX〗Z〖WTBZ〗+,得到任意分数阶的微分方程比较定理,从而扩大了含Riemann-Liouville导数的分数阶微分方程比较定理的使用范围.

Abstract: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.