**Yuji Liu**

##
Solvability of Periodic Boundary Value Problems of Fractional Differential
Systems with Impulse Effects

**abstract:**

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