Hristov J.2024-07-102024-07-102024-07-102024-07-102015-01-010354-983610.2298/TSCI130803151HSCOPUS_ID:84979917090https://rlib.uctm.edu/handle/123456789/398This work presents an attempt to apply the integral-balance approach to diffusion models with fading memories expressed by weakly singular kernels. It demonstrates how three integration techniques (heat-balance integral method, double-integration method, and frozen front approach) work with a general parabolic profile with unspecified exponent and result in closed-form solutions. The main steps are exemplified by solutions where the fading memory is represented by Volterra integrals and by a time-fractional Riemann-Liouville derivative.enArticle