New results of global existence and uniqueness for fuzzy fractional integro-differential equations

Abstract

 Fractional calculus and fuzzy set theory together provide a powerful framework for modeling complex systems with memory and uncertainty. However, existing studies on fuzzy fractional differential equations often suffer from an improperly defined solution space and rely on restrictive assumptions such as Lipschitz continuity. In this work, we correct these issues by first establishing existence and uniqueness for fuzzy fractional integral equations under weaker conditions. We then introduce a general fuzzy fractional integro-differential equation combining Riemann-Liouville derivatives with Volterra and Fredholm operators. Using the monotone iterative technique with upper and lower solutions, we obtain global existence and uniqueness results that significantly relax previous hypotheses, providing a more solid theoretical foundation for this emerging field.