分数阶时滞微分方程的Hyers-Ulam稳定性

Hyers-Ulam Stability of Fractional Delay Differential Equations

本文致力于研究非齐次分数阶时滞微分方程的Hyers-Ulam稳定性,其中阶数α∈(0,1).首先我们利用时滞型Mittag-Leffler矩阵函数,通过拉普拉斯变换方法找到了非齐次分数阶时滞微分方程的解的表达式.进一步地,我们证明了非齐次分数阶时滞微分方程在区间[0,T]上是Hyers-Ulam稳定的.最后,我们通过一个例子说明了结果的正确性.

This paper is devoted to the Hyers-Ulam stability of the inhomogeneous fractional delay differential equations with orderα∈(0,1).On the basis of the delayed Mittag-Leffler matrix function,we give the explicit solution of the inhomogeneous delay fractional differential equations by using the technique of Laplace transforms.Furthermore,we prove the inhomogeneous delay fractional differential equations satisfy the Hyers-Ulam stability in the finite time interval[0,T].Finally,an example is presented to illustrate our theoretical results.