Abstract: Some kind of abstract Volterra linear integral operators is studied in order to solve the boundary value problems of abstract kinetic equation. The solving process is named as integral operator solving process, thus it is fended provide a new, simple and immediate solving process of the boundary value problems of abstract kinetic equations. In the paper we solve the boundary value problems of abstract kinetic equation with a parameter and reflecting boundary condition by the integral operator solving process.

Key words: the boundary value problem of abstract kinetic equation, abstract Volterra integral operator, integral operator solving process, reflecting boundary condition