MULTIPLE SOLUTIONS FOR <i>P</i>-LAPLACIAN FRACTIONAL DIFFERENTIAL EQUATIONS WITH <i>ψ</i>-CAPUTO DERIVATIVE AND IMPULSIVE EFFECTS

In this study, we consider the multiplicity of solutions for a new class of $p$-Laplacian fractional differential equations involving $\psi$-Caputo fractional derivative with instantaneous and non-instantaneous impulses. Since the $p$-Laplacian operator, $\psi$-Caputo fractional derivative and impulsive effects exist at the same time, it is difficult to establish the variational structure of the considered problem. By virtue of critical point theorems and variational methods, we give some new criteria to guarantee that the problem has at least two weak solutions and infinitely many weak solutions. Some recent results are improved and extended.