Abstract

In this reserach work, we consider an initial value problem for a linear matrix coefficients system of fractional-order differential equations with multiple constant delays in the sense of Caputo. First, we derive anexplicit analytical solution for linear inhomogeneous fractional multi-delay differential equations of order0 < α < 1. The obtained results are covering the corresponding results for first-order differential systemswith multiple constant delays. Second, we prove the global existence and uniqueness of the solution of anonlinear time-delay system with fractional-order using the principle of contraction mapping in a weightedspace of continuous functions. We analyze finite-time stability for a class of fractional-order differentialequations with multiple delays. We derive some sufficient conditions for the finite-time stability based ona multi-delayed perturbation of the Mittag-Leffler type matrix function by virtue of Gronwall’s integralinequality. Finally, we demonstrate the validity of the developed technique and discuss it with numericalexamples.