Existence and Stability of a Coupled ( k , ϖ )–Hilfer Fractional System With Substrip and Multipoint Boundary Conditions via Darbo’s Fixed Point Approach

This paper investigates a nonlinear coupled system of ( k , ϖ )‐Hilfer fractional integro‐differential equations with substrip and multipoint boundary conditions. A coupled measure of noncompactness is introduced on the product weighted space . Darbo’s fixed point theorem, combined with this measure, yields existence results under standard Lipschitz and growth assumptions. The Darbo constant is estimated explicitly using ( k , ϖ )‐gamma functions. This is the first work combining ( k , ϖ )‐Hilfer operators, substrip and multipoint conditions, and Darbo’s theorem with a coupled measure of noncompactness. Uniqueness follows from the Banach contraction principle. Ulam–Hyers stability is established with explicit constants. Several special cases are recovered: Caputo, classical Hilfer, Hadamard, Katugampola, and their k ‐analogs. Numerical examples support the theoretical findings. The proposed framework avoids the strong compactness assumptions typically required by classical fixed point theorems.