<p>This study presents a comprehensive mathematical framework for modeling thermoelastic and thermodiffusive processes in fractal spherical tumor media, integrating the Moore–Gibson–Thompson (MGT) heat conduction theory with nonlocal elasticity and memory-dependent derivatives. The biological complexity of tumor tissue is captured via non-integer dimensional geometry, allowing for precise representation of radial transport phenomena. By incorporating kernel-based memory effects and Eringen’s nonlocal stress model, the coupled bioheat diffusion equations address the limitations of classical Fourier and Fick laws. The formulation includes generalized vector operators and Laplace-transformed governing equations to determine the distributions of displacement, temperature, concentration, stress, and chemical potential. Numerical inversion using the Gaver–Stehfest algorithm enables time-domain simulations, which elucidate the interplay between memory effects, nonlocal interactions, and fractal structure in biological systems. This work introduces a unified fractal–fractional framework for modeling thermoelastic diffusion in spherical tumor shells, offering methodological novelty and biomedical relevance to hyperthermia, cryotherapy, and drug delivery.</p>