Title: Carleman estimates for the time-fractional advection-diffusion equations and applications,
Abstract: In this article, we prove Carleman estimates for the generalized
time-fractional advection-diffusion equations by considering the fractional
derivative as perturbation for the first order time-derivative. As a direct
application of the Carleman estimates, we show a conditional stability of a
lateral Cauchy problem for the time-fractional advection-diffusion equation,
and we also investigate the stability of an inverse source problem.