Existence and uniqueness results for a new class of coupled Urysohn–Hammerstein-type Ψ-Katugampola fractional integral equations

In this paper, we study a new class of coupled nonlinear fractional integral equations involving the Ψ-Katugampola fractional integral operator. By applying Dhage’s fixed point theorem in a Banach algebra, we establish sufficient conditions for the existence of solutions to the proposed coupled system and prove uniqueness via the Banach contraction principle. The obtained results extend and generalize several known existence results for fractional integral equations associated with particular choices of the kernel. An illustrative example is presented to demonstrate the applicability of the main theorem.