  Non-local equations of motion contain an infinite number of derivatives and
commonly appear in a number of string theory models. We review how these
equations can be rewritten in the form of a diffusion-like equation with
non-linear boundary conditions. Moreover, we show that this equation can be
solved as an initial value problem once a set of non-trivial initial conditions
that satisfy the boundary conditions is found. We find these initial conditions
by looking at the linear approximation to the boundary conditions. We then
numerically solve the diffusion-like equation, and hence the non-local
equations, as an initial value problem for the full non-linear potential and
subsequently identify the cases when inflation is attained.
