On a Nonlinear Coupled Fractional Differential System With Multiderivative-Terms and Coupled Closed Boundary Data

This article is devoted to the study of existence, uniqueness, and Ulam–Hyers stability for a coupled system of two nonlinear Caputo-type multiterm fractional differential equations equipped with coupled closed boundary data. The concept of coupled closed boundary conditions finds its applications in several physical situations, like composite panels, honeycomb lattices, deblurring problems, etc. The nonlinear multiterm Caputo–type coupled fractional differential systems are significant due to their occurrence in hydrodynamics, fractional diffusion phenomenon, fluid dynamics, and other factors. We apply the standard tools of the fixed point theory (Leray–Schauder’s alternative and Banach’s fixed point theorem) to accomplish the desired results. Numerical examples illustrating the obtained results are offered. Our results are new in the given setting, and several new results appear as their special cases.