A class of piecewise fractional functional differential equations with impulsive

In this paper, we study a class of piecewise fractional functional differential equations with impulsive and integral boundary conditions. By using Schauder fixed point theorem and contraction mapping principle, the results for existence and uniqueness of solutions for the piecewise fractional functional differential equations are established. And by using cone stretching and cone contraction fixed point theorems in norm form, the existence of positive solutions for the equations are also obtained. Finally, an example is given to illustrate the effectiveness of the conclusion.