Ulam--Hyers Stabilization of New Fuzzy Fractional Partial Differential Coupled Systems Involving Caputo--Katugampola Generalized Hukuhara Type Differentiability

In this paper, we study existence and stability of solutions for a class of new coupled systems of fuzzy fractional partial differential equations involving Caputo--Katugampola and generalized Hukuhara (gH-) type derivatives, which provides a solid theoretical foundation and effective analytical tools for scientific research and engineering practice to address highly complex, uncertain, and memory-dependent interacting systems. Under some suitable assumptions that break through the limitations of traditional Lipschitz conditions, existence of classical solutions of the coupled systems is strictly proved by innovatively applying Schauder fixed point theorem. Furthermore, the existence of two kinds of gH-type weak solutions is confirmed by constructing typical examples. Further, stability of the fuzzy fractional partial differential coupled systems is analyzed based on Ulam--Hyers stability theory.