  In the paper, the initial-boundary value problems to a semilinear
integro-differential equation with multi-term fractional Caputo derivatives are
analyzed. A particular case of this equation models oxygen diffusion through
capillaries. Under proper assumptions on the coefficients and a nonlinearity,
the longtime behavior (as $t\to+\infty$) of a solution is discussed. In
particular, the existence of absorbing sets in suitable functional spaces is
established.
