A Coupled Discrete Fractional Difference System with a New Class of Coupled Multi-Point Closed Boundary Conditions

In this article, a nonlinear coupled system involving Caputo difference operators of distinct orders subject to novel coupled boundary conditions is studied. Existence and uniqueness solutions are established by applying the standard fixed-point theorem under suitable assumptions. The stability behavior of the considered system is analyzed using the Hyers–Ulam stability approach, and sufficient limitations ensuring the stability of the results are obtained. To demonstrate the validity of the theoretical solutions, two illustrative examples are presented. The first example introduces the assumptions required for the existence, uniqueness, and stability results. The second example verifies a financial discrete coupled system solved numerically via a discrete iterative method. Numerical simulations are performed for different fractional orders to examine the influence of memory effects on solution dynamics.