Abstract: The stability of a fractional degenerate differential system with delay is considered. Firstly, according to the Laplace transform method for the Caputo fractional derivatives, the stability conditions for the degenerate differential system with multiple-delays under different Caputo derivatives are derived and the corresponding criterions are given in different cases. Secondly, by using the roots of the characteristic equation, the all-delays stability of fractional degenerate differential systems are analyzed and some sufficient conditions are obtained. Some results generalize the corresponding results of the fractional differential system. Finally, some examples are presented to illustrate the validity of theorems.

Key words: stability, degenerate differential equation, fractional order, delay