Fractional $p$-Laplacian equations with sandwich pairs

Abstract

The main purpose of this paper is to consider new sandwich pairs and investigate the existence of solution for a new class of fractional differential equations with $p$-Laplacian via variational methods in $\psi$-fractional space $\mathbb{H}^{\alpha,\beta;\psi}_{p}(\Omega)$. The results obtained in this paper are the first to make use of the theory of $\psi$-Hilfer fractional operators with $p$-Laplacian.