AUTHOR=Vasylyeva Nataliya 

TITLE=Semilinear multi-term fractional in time diffusion with memory

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=10

YEAR=2024

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1388414

DOI=10.3389/fams.2024.1388414

ISSN=2297-4687

ABSTRACT=<p>In this study, the initial-boundary value problems to semilinear integro-differential equations with multi-term fractional Caputo derivatives are analyzed. A particular case of these equations models oxygen diffusion through capillaries. Under proper requirements on the given data in the model, the classical and strong solvability of these problems for any finite time interval [0, <italic>T</italic>] are proved via so-called continuation method. The key point in this approach is finding suitable a priori estimates of a solution in the fractional Hölder and Sobolev spaces.</p>