A Yamazaki-type estimate to a space-time fractional diffusion equation

In this work, we develop the Yamazaki inequality and estimates of the Mittag-Leffler family associated with the space-time fractional diffusion equation in Lp-weak spaces. This result generalizes the inequality given by Yamazaki (2000) for the heat semigroup, which was generalized by Ferreira and VillamizarRoa (2006) for heat semigroup associated with the fractional Laplacian, and Caicedo et al (2021) for the Mittag-Leffler family associated with the time-fractional diffusion equation.