Research on the Existence and Uniqueness of Solutions to Fractional Diffusion Equations with Three-Parameter Damping Terms

This paper investigates a fractional diffusion equation incorporating a three-parameter damping. By employing a generalized Mittag–Leffler function alongside the associated Riemann–Liouville resolvent family, we establish the well-posedness of strong solutions. This model extends the classical two-parameter undamped case, thereby ensuring consistency with the existing theoretical framework.