TOPOLOGICAL DEGREE FOR GENERALIZED CAPILLARITY PHENOMENA INVOLVING FRACTIONAL ψ-HILFER DERIVATIVE WITH THE τ( ⋅ )-LAPLACIAN

We study a nonlinear eigenvalue problem governed by the ψ-Hilfer fractional derivative, arising in the context of capillarity theory with Dirichlet boundary constraints. The nonlinearity involved generally fails to meet Ambrosetti–Rabinowitz-type growth conditions. To address this, we develop a framework that combines pseudomonotone operator theory with variational methods in fractional ψ-Hilfer Sobolev spaces, proving the existence of weak solutions.