含变系数的线性分数阶微分方程的解析解(英文)

Analytic Solutions to Varying Coefficient Linear Fractional Differential Equations

本文利用算子级数给出了含变系数线性分数阶微分方程的解析解,并通过几个例子说明了解析表达式的重要性.另外,我们还得到了分数阶Gronwall不等式的微分形式和积分形式,它们是经典Gronwall不等式的推广.

In this paper, we give analytic solutions to varying coefficient linear fractional dif- ferential equations in terms of operator series. Several examples illustrate the use- fulness of the proposed analytic expressions. Gronwall＇s differential and integral inequalities for fractional differential equations are obtained. These inequalities are extensions of the classical Gronwall＇s differential and integral inequalities.