Differential equation associated with involutions

In this paper, we consider with a class of system of differential equations whose argument transforms are involutions. In this an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. Then either two initial conditions are necessary for a solution; the equation is then reduced to a boundary value problem for a higher order ODE.

Keywords: involution, linear differential equation, fixed point, boundary value problem