论文标题
分数线性时间延迟系统及其ULAM-HYERS稳定性的分析解决方案
Analytical solution of the fractional linear time-delay systems and their Ulam-Hyers stability
论文作者
论文摘要
我们介绍了延迟的mittag-leffler型矩阵函数，延迟的分数余弦，延迟的分数正弦，并使用拉普拉斯变换来获得IVP的分析解决方案，用于Hilfer类型的分数线性时间 - 延迟系统$ d_ {0，t} +ωz\ left（t-h \ right）= f \ left（t \右）$ $ 1 <μ<2 $和类型$ 0 \leqν\ leq1，$，带有不可渗透的矩阵$ a $ a $ and $ω$。此外，我们研究了Hilfer型分数线性时间延迟系统的ULAM-HYERS稳定性。获得的结果扩展了Caputo和Riemann-Liouville型分数线性时间延迟系统的结果，甚至对于这些分数延迟系统即使是新的。
We introduce the delayed Mittag-Leffler type matrix functions, delayed fractional cosine, delayed fractional sine and use the Laplace transform to obtain an analytical solution to the IVP for a Hilfer type fractional linear time-delay system $D_{0,t}^{μ,ν}z\left( t\right) +Az\left( t\right) +Ωz\left( t-h\right) =f\left( t\right) $ of order $1<μ<2$ and type $0\leqν\leq1,$ with nonpermutable matrices $A$ and $Ω$. Moreover, we study Ulam-Hyers stability of the Hilfer type fractional linear time-delay system. Obtained results extend those for Caputo and Riemann-Liouville type fractional linear time-delay systems and new even for these fractional delay systems.
