The Periodic Solutions of the Compound Singular Fractional Differential System with Delay

The paper gives sufficient conditions on the existence of periodic solution for a class of compound singular fractional differential systems with delay, involving Nishimoto fractional derivative. Furthermore, for the particular functions, the necessary conditions on the existence of periodic solution are also derived. Especially, for two-dimensional compound singular fractional differential equation with delay, the criteria of existence of periodic solution are obtained. Finally, two examples are presented to verify the validity of criteria.