Measure Neutral Functional Differential Equations as Generalized ODEs

In this paper, we introduce a class of measure neutral functional differential equations of type $$\begin{aligned} \mathrm {D}[N(x_t,t)]=f(x_t,t)\mathrm {D}g(t) \end{aligned}$$ through the relation with a certain class of generalized ordinary differential equations introduced in Federson and Schwabik (Differ Integral Equ 19(11):1201–1234, 2006) (we write generalized ODEs), using similar ideas to those of Federson et al. (J Differ Equ 252(6):3816–3847, 2012). By means of the correspondence with generalized ODEs, we state results on the existence, uniqueness and continuous dependences of solutions for our equation of neutral type.