Existence and multiplicity of solutions to a ψ-Hilfer fractional p-Laplacian equations

Abstract

In this paper, by Symmetric Mountain Pass Lemma, we study the existence and multiplicity of solutions to the following nonlocal [Formula: see text]-Hilfer fractional [Formula: see text]-Laplasian equation: [Formula: see text] where [Formula: see text] and [Formula: see text] are [Formula: see text]-Hilfer fractional derivatives left-sided and right-sided of order [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] and [Formula: see text] are [Formula: see text]-Riemann–Liouville fractional integrals left-sided and right-sided, [Formula: see text] and [Formula: see text] are continuous functions. Finally, we give some examples to illustrate the main results.