<p>Motivated by the abundance of fractals within the natural world, the present study deals with a novel extension of classical thermoelasticity to fractal materials by formulating a generalized vector calculus in non-integer dimensional spaces. Fractal media, characterized by complex geometries and anomalous transport behavior, are modeled as continua with non-integer mass dimensions. We develop a comprehensive thermoviscoelastic diffusion framework that incorporates nonlocal elasticity, fractional-order derivatives, and a three-phase-lag heat conduction model. The physical system considered is an infinitely extended Kelvin–Voigt viscoelastic medium with a cylindrical cavity subjected to time-dependent thermal and chemical boundary conditions. The governing equations are transformed into the Laplace domain and solved analytically, with time-domain solutions obtained via Zakian numerical inversion. Numerical simulations reveal the significant influence of fractal geometry, nonlocal effects, and fractal operators on temperature distribution, stress evolution, and diffusion behavior. These findings offer valuable insights for the design of advanced materials and nanoscale systems where classical models fall short.</p>