Volterra–Stieltjes integral equations and impulsive Volterra–Stieltjes integral equations

Abstract

In this paper, we prove existence and uniqueness of solutions of Volterra–Stieltjes integral equations using the Henstock–Kurzweil integral. Also, we prove that these equations encompass impulsive Volterra–Stieltjes integral equations and prove the existence and uniqueness for these equations. Finally, we present some examples to illustrate our results.

Keywords

• volterra–stieltjes integral
• impulsive equations
• existence and uniqueness
• henstock–kurzweil–stieltjes integral