Pressure control system with nonlocal friction

We analyze the motion of a pressure control system described by a differential equation with nonlocal dissipative force. This system is composed by an oscillator, a membrane and a constant force. We consider the dissipative memory kernel consisting of two terms. One of them is described by the Dirac delta function which represents a local friction, whereas for the second one we consider two types: the exponential and power-law functions which represent nonlocal dissipative forces. For these cases, one can obtain exact solutions for the displacement and velocity. The long-time behaviors of these quantities are also investigated.