Smart grids have made power systems to be efficient, reliable and sustainable thus the importance of integrating smart grids into F-differential equation to F-boundary problem necessitates the use of important techniques of which fuzzy integral transforms is an imporcott method. The study extends the formula of third-order fuzzy derivative of FFWT based on which it can determine its generalized nth-order fuzzy derivative capability. The manipulation is done over a research structure based on highly generalized Hukuhara differentiability. The drug distribution measurement reveals drug body level that appears as the ratio of plasma or blood drug quantity to entire body drug quantity and by the same token, the addressed fuzzy FFW-transform solves drug concentration in organ equations.