System of Nonlinear (<i>k</i>, ψ)-Hilfer Fractional Order Hybrid Boundary Value Problems

This paper focuses on the existence and uniqueness of solutions for a new class of coupled fractional differential equations subject to specific boundary conditions. We introduce a novel approach that incorporates the (k, ψ)-Hilfer fractional derivative, a recent advancement in fractional calculus. By leveraging the properties of this operator, we develop a comprehensive framework to analyze the proposed system. Our findings, established through the application of Schauder's fixed point theorem and the Banach contraction principle, contribute to the understanding of complex phenomena modeled by fractional differential equations. This research expands the boundaries of fractional calculus and offers potential applications in various scientific and engineering domains.