A Hilbert Space Perspective on Ordinary Differential Equations with   Memory Term
  We discuss ordinary differential equations with delay and memory terms in Hilbert spaces. By introducing a time derivative as a normal operator in an appropriate Hilbert space, we develop a new approach to a solution theory covering integro-differential equations, neutral differential equations and general delay differential equations within a unified framework. We show that reasonable differential equations lead to causal solution operators. 
Anke Kalauch, Rainer Picard, Stefan Siegmund, Sascha Trostorff and   Marcus Waurick
math.CA