$\psi$-Appell polynomials` solutions of an umbral difference   nonhomogeneous equation
  One discovers why the solution of generalized umbral calculus difference nonhomogeneous equation in the form recently proposed by the author extends here now to generalized appellian delta operator and corresponding polynomials case almost automatically. The reason for that is just the proper framework of the generalized finite operator calculus recently being developed by the present author. 
A.K.Kwasniewski