Existence of weak solutions for double phase fractional problems with variable exponents

Abstract

In this present paper, we are first of all interested in some continuity and compactness results for the space ψ-fractional 𝕊 𝒜 α , β ; ψ ⁢ ( Λ ) {\mathbb{S}^{\alpha,\beta;\psi}_{\mathcal{A}}(\Lambda)} . In this sense, we investigate the existence of at least two solutions with constant signs using truncation arguments and comparison methods of a new class of fractional differential equations with m ⁢ ( ξ ) {m(\xi)} -Laplacian with double phase.