Existence and Nonexistence of Nontrivial Solutions for Fractional Advection–Dispersion Equation with Instantaneous and Non-Instantaneous Impulses

In this paper, we consider a class of fractional advection–dispersion equations involving instantaneous and non-instantaneous impulses. The existence of nontrivial solutions is established via Bonanno and D’Aguì’s critical point theorem. Under suitable conditions, we further prove the nonexistence of nontrivial solutions, which is the new result. Additionally, the application of our main results is demonstrated through two examples.