Long and Short Time Behavior of Non-local in Time Subdiffusion Equations

This paper is devoted to studying the long and short time behavior of the solutions to a class of non-local in time subdiffusion equations. To this end, we find sharp estimates of the fundamental solutions in Lebesgue spaces using tools of the theory of Volterra equations. Our results include, as particular cases, the so-called time-fractional and the ultraslow reaction-diffusion equations, which have seen much interest during the last years, mostly due to their applications in the modeling of anomalous diffusion processes.