Abstract:

The boundary value problem of the fractional impulsive differential equation was studied by means of the nonlinear functional theory. Some existence theorems of positive solutions for the boundary value problem of fractional impulsive differential equation with Caputo derivative were proved with the help of the fixed point theorem of cone expansion and compression of norm type, obtaining the sufficient conditions about the existence of positive solutions and the relevant corollary.

Key words:  positive solutions, Caputo derivative, fractional impulsive differential equation, fixed point theorem