Positive solutions for a class of Hilfer–Hadamard fractional differential equations under interdependent integral boundary conditions

This study explores the necessary and sufficient conditions for the existence and uniqueness of positive solutions to boundary value problems involving a class of nonlinear fractional differential equations of the Hilfer–Hadamard derivative with interdependent boundary conditions. We study the properties of γ-concave and subhomogeneous operators to obtain our results, which are stated in terms of a fixed-point theorem. Furthermore, we provide an illustrative example to validate our theoretical findings and demonstrate their practical implications. The novelty of our work lies in the investigation of interdependent integral boundary conditions distinct from those found in previous literature. This innovative approach enables a deeper understanding of the dynamics involved in these complex systems.