EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR THE FRACTIONAL DIFFERENTIAL EQUATIONS WITH <i>P</i> -LAPLACIAN IN <inline-formula><tex-math id="M1">$ \mathbb{H}^{\nu,\eta;\psi}_{p}$</tex-math></inline-formula>

Abstract

<abstract> This present paper is dedicated to investigate the existence, uniqueness and minimization properties of weak solutions for a fractional differential equation in the sense of the $\psi$-Hilfer fractional operator, with $p$-Laplacian in the $\psi$-fractional space $\mathbb{H}^{\nu, \eta;\psi}_{p}$. To obtain such results, we use a variational structure for the main operator of the problem and the Harnack inequality. </abstract>