Measure functional differential equations of the form \[ x(t)=x(t_0)+\int_{t_{0}}^tf(x_s,s)dg(s),\quad t\in [t_0,t_0+\sigma],\quad x(t_0)=\phi \] and impulsive measure functional differential equations of the form \[ x(t)=x(t_0)+\int_{t_{0}}^tf(x_s,s)dg(s)+\sum_{k\in\{1,\dotsc,m\}, t_{k}<t}I_k(x(t_{k})), \quad t\in [t_0,t_0+\sigma],\quad x(t_0)=\phi \] are studied, where the integrals on the right-hand side are the Kurzweil-Henstock-Stieltjes integrals with respect to a nondecreasing function \(g\).
The relation between measure functional differential equations, impulsive measure functional differential equations and impulsive functional dynamic equations on time scales is described. Existence and uniqueness of solutions, continuous dependence and periodic averaging for both types of impulsive measure functional differential equations are presented. The paper is a continuation of the author’s paper [J. Differ. Equations 252, No. 6, 3816–3847 (2012; Zbl 1239.34076)].