On solutions related to FitzHugh-Rinzel type model

A ternary autonomous dynamical system of FitzHugh-Rinzel type is analyzed. The system, at start, is reduced to a nonlinear integro differential equation. The fundamental solution $H(x,t)$ is explicitly determined and the initial value problem is analyzed in the whole space. The solution is expressed by means of an integral equation involving $H(x,t)$. Moreover, adding an extra control term, explicit solutions are achieved.