On a Class of Generalized Capillarity Phenomena Involving Fractional $\psi$-Hilfer Derivative with $p(\cdot)$-Laplacian Operator
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Authors: E. ARHRRABI AND H. EL−HOUARI
DOI: 10.46793/KgJMat2606.885A
Abstract:
This research delves into a comprehensive investigation of a class of ψ-Hilfer generalized fractional nonlinear eigenvalue equation originated from a capillarity phenomenon with Dirichlet boundary conditions. The nonlinearity of the problem, in general, do not satisfies the Ambrosetti-Rabinowitz (AR) type condition. Using critical point theorem with variational approach and the (S+) property of the operator, we establish the existence of positive solutions of our problem with respect to every positive parameter ξ in appropriate fractional ψ-Hilfer spaces. Our main results is novel and its investigation will enhance the scope of the literature on differential equation of fractional ψ-Hilfer generalized capillary phenomena.
Keywords:
Generalized ψ-Hilfer derivative, Capillary phenomenon, critical point theorem, variational approach, (S+) property.
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