Existence of solutions for boundary value problems of fractional impulsive differential equations with Hilfer

In order to extend the basic theory of boundary value problems, the existence of solutions for a class of Hilfer fractional impulsive differential equations with finite impulsive points was studied. Firstly, the integral equation equivalent to the differential equation was obtained; Secondly, appropriate Banach spaces and norms were defined, and appropriate operators were constructed. When the nonlinear term satisfies different conditions, sufficient conditions for the existence of solutions of such boundary value problems were obtained by using Krasnoselskii fixed point theorem; Finally, two examples were used to illustrate the universality of the research results. It is shown that the solution of the boundary value problem of impulsive differential equations with Hilfer fractional derivative exists. By using the Krasnoselskii fixed-point theorem, the existence of solutions for impulsive differential equation boundary value problems with Hilfer fractional order can be effectively solved, which provides some reference for solving other types of impulsive fractional differential equation boundary value problems.