Semilinear multi-term fractional in time diffusion with memory.

This article explores the solvability of semilinear multi-term time-fractional diffusion equations with memory, specifically focusing on modeling the diffusion of oxygen through capillaries. The study utilizes a continuation method and a priori estimates to prove the classical and strong solvability of these problems within a finite time interval. The article discusses suitable conditions on the given data and coefficients to ensure solvability, as well as different assumptions and approaches for one-dimensional and multidimensional cases. The research also suggests potential applications of the technique to analyze inverse problems and fully nonlinear equations. [Extracted from the article]