Exact Solution And Hyers-Ulam Stability Of A Class Of Fractional Delay Differential Systems

In this paper,the exact solutions and Hyers-Ulam stability of a class of n-dimensional Caputo fractional differential systems with multiple delays are considered.Firstly,the applicability of Laplace transform to the target system is verified and the feasibility theorem of Laplace transform is obtained.With this effective tool of Laplace transform,the exact solution of the fractional differential system with pure delay is given and the corresponding delay matrix functions are obtained.By applying the multinomial theorem for noncommutative matrices,the related result was extended to the multi-delay case without a commutativity assumption on the matrix coefficients,and the representation of exact solution and the corresponding delay matrix functions of the multi-delay system are established.Finally,based on the obtained results,the Hyers-Ulam stability of the system in finite time is investigated.Without any restrictions on the matrix coefficients of the linear part,our works partially improve previous results in the field of fractional delay differential equations.