Boundary‐integral analysis of multi‐term fractional heat conduction in heterogeneous media

Abstract A rigorous boundary‐integral framework is developed for the numerical solution of multi‐term time‐fractional heat conduction in heterogeneous and nano‐engineered media. The governing model employs several Caputo time derivatives to represent multi‐scale thermal relaxation and nonlocal memory effects that arise in layered and microstructured solids, where classical Fourier theory fails. By transforming the fractional evolution equation into the Laplace domain, the problem is recast into a modified Helmholtz equation whose fundamental solution enables an exact boundary integral representation. This formulation leads to a boundary‐only discretization, reducing the spatial dimension of the problem and providing high accuracy in unbounded, semi‐infinite, and strongly layered domains. A complete boundary element method (BEM) is constructed in the Laplace domain, including treatment of nonhomogeneous terms and efficient numerical inversion of the transform using Durbin's algorithm to recover the transient response. The obtained method is unconditionally stable with respect to fractional orders and maintains accuracy over broad time scales, from short‐time transients to long‐time memory effects. Systematic numerical tests are carried out to analyze the effect of fractional parameters, material thickness, and localized heat sources on temperature and heat flux distributions. The method reproduces the classical diffusion limit and reveals the subdiffusive regimes characteristic of anomalous transport. The proposed formulation combines the analytical structure of fractional mechanics with the computational advantages of boundary‐only discretization. It provides a general and scalable tool for multi‐term fractional diffusion problems in mechanics, with relevance to layered and nano‐structured solids subjected to intense transient loading. Beyond thermal applications, the framework is directly extensible to a broad class of fractional transport and field equations encountered in contemporary continuum mechanics.