VARIATIONAL APPROACH TO MIXED BOUNDARY VALUE PROBLEMS OF FRACTIONAL STURM-LIOUVILLE DIFFERENTIAL EQUATIONS WITH INSTANTANEOUS AND NON-INSTANTANEOUS IMPULSES

This paper investigates a class of fractional Sturm-Liouville differential equations with mixed boundary conditions, which are subjected to parameter and impulsive perturbations (including instantaneous and non-instantaneous impulses). By employing the variational methods and critical point theorems, we derive several criteria that guarantee the existence of at least one and two classical solutions, respectively, when the parameters fall within different intervals. Furthermore, we provide an example to demonstrate the effectiveness of our main results.