Abstract: The representation problem of general solutions of hybrid linear fractional-order differential systems with multiple time delays was discussed. Based on Gronwall-Bellman integral inequality, the exponential estimates of the solutions of this equation were derived. The general solution to hybrid linear homogeneous fractional-order differential equations with multiple time delays was derived by means of the fundamental solution of the homogeneous systems and the Laplace transform method, then the general solution of the nonhomogeneous systems was obtained by means of Laplace inverse transform and convolution theorem.

Key words: hybrid fractional-order linear systems, multiple time delays, fundamental solution, general solution, Laplace transform