<p>This paper begins with a concise summary of fractal calculus, laying out the foundational concepts necessary for further analysis. We then introduce the fractal Rosenau–Burgers equation and present its analytical solution. Perturbation methods for solving this nonlinear fractal differential equation are developed and examined in detail. Building upon this framework, we investigate practical applications such as signal propagation in fractal transmission lines and transport phenomena in porous and fractal media. Additionally, we provide graphical illustrations of the solutions to demonstrate the effects of fractal spatial and temporal dimensions on these models.</p>