Two new classes of periodic boundary value problems of coupled impulsive fractional differential equations are proposed. Sufficient conditions are given for the existence of solutions of these problems. The analysis relies on the well known Schauder's fixed point theorem. The obtained results show that the Riemann-Liouville fractional derivative and the Caputo's fractional derivative have similar properties. Examples are given to illustrate the main theorems.
Mathematics Subject Classification: 92D25, 34A37, 34K15
Key words and phrases: Singular fractional differential system, Riemann-Liouville fractional derivative, Caputo's fractional derivative, impulsive periodic boundary value problem, fixed point theorem