A SINGULAR Ψ-HILFER GENERALIZED FRACTIONAL DIFFERENTIAL SYSTEM PROBLEMS WITH \(p(\cdot )\)-LAPLACIAN OPERATOR

In this paper, we study the existence and multiplicity of solutions for a singular system problem involving the \(\psi\) $\psi$ -Hilfer fractional derivative with the \(p(\cdot )\) $p(·)$ -Laplacian operator. Employing the Nehari manifold together with a variational approach, we establish the existence and multiplicity of positive solutions to our problem. These results will enhance the scope of the literature on coupled systems of \(\psi\) $\psi$ -Hilfer fractional differential equations with Dirichlet-type boundary conditions.