Fractional ψ-Hilfer derivative spaces: study of Kirchhoff problem with p(•)-Laplacian operator

Abstract

The paper focuses on the existence and multiplicity of weak solutions to the nonlinear Kirchhoff-type equations involving ψ-Hilfer derivatives with p(・)-Laplacian operators and Dirichlet boundary conditions. Through the application of a critical point approach, along with genus theory and variational techniques, we establish the existence of infinitely many positive solutions within appropriate ψ-Hilfer fractional derivative spaces. Our novel main results contribute to the advancement of the literature on differential equations involving the ψ-Hilfer fractional derivative.