Existence and stability of a mild solution to an abstract sequential time-fractional diffusion equation of pantograph type

This article studies a sequential time-fractional diffusion equation characterized by the Caputo derivative. We establish the existence of a mild solution using the resolvent operator and Schaefer’s fixed point technique. Moreover, we explore Ulam-Hyers and Ulam-Hyers-Rassias stabilities through nonlinear methods. The study also presents examples of applications of these techniques, such as application to a partial Caputo time-fractional diffusion equation.