This article is devoted to consider homotopy analysis method (HAM) for discontinued problems arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a nonlinear differential -difference model is considered as an alternative approach to describing discontinued problems. This procedure is powerful tool for solving large amount of problems. Using this method, it is possible to find the exact solution or an approximate solution of the problem. This technique provide a series of functions which may converges to the exact solution of the problem. The comparison of the approximate solution with the exact solution and the Adomian decomposition method reveals that the proposed method is an attractive method in solving the differential-difference equations.