<p>This paper delves into the exploration of direct and inverse problems pertaining to the time-fractional heat equation featuring a time-dependent leading coefficient for positive operators. Initially, we address the direct problem, where we establish the unique existence of the generalized solution and derive various regularity results. Subsequently, we focus on the inverse problem aimed at determining the leading coefficient. Through the utilization of insights gleaned from the direct problem, we demonstrate the Lipschitz stability result for this inverse problem.</p>