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

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∈Z+,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 order a of the comparison theorem is extended from a E （0,1） to a （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.