On the analytical separation of variables solution for a class of partial integro-differential equations

The present work deals with the derivation of analytical solutions for a particular class of partial intregro-differential equations, by employing the separation of variables technique. The equation under consideration consists of parabolic and hyperbolic terms, so that the character of the equation is determined by their relative weight. The key feature for the analysis presented here is that the eigenfunctions of the problem, which can be found in a closed form, do not comprise an orthogonal set of functions. The convergence of the new series solution is getting faster as the parabolic term of the integro-differential equation dominates over the hyperbolic (integral) one.