This chapter explores the way to model the movement of nanoparticles, especially in drug diffusion, using non-linear time-fractional Klein–Gordon equations (TFKG). Such an equation is very helpful for understanding the behavior of nanoparticles in biological systems and porous materials, which is the key to effective drug delivery. We introduce a new numerical method called the Laplace Homotopy Perturbation Method (LHPM) that combines the use of Laplace transforms with homotopy techniques to handle such complex equations. In this chapter, we demonstrate the working of LHPM and apply it to a number of examples associated with drug diffusion and nanoparticle movement. Analysis will include numerical values as well as elaborate graphs in order to exhibit the solution behavior. Hence, by comparison of such numerical solutions with the exact results, it establishes that the LHPM is reliable method about how delivery of drugs from nanoparticles can accurately be accounted for tissues. Therefore, this chapter has some essential implications regarding potential use to enlighten mechanisms of nanoparticles in their applications within the modern drug delivery system among scientists working within quantum technology or plasma physics domains.