Existence of Mild Solutions for Fuzzy Fractional Evolution Equations via Schauder Fixed Point Theorem

This paper establishes a novel and unified existence theory for mild solutions to a class of fuzzy fractional evolution equations governed by the \psi-Caputo generalized Hukuhara (gH) derivative. The considered system is distinctive for its incorporation of a Volterra-type integral term within the nonlinearity, introducing a cumulative memory effect and is analyzed within a semigroup framework on the space of triangular fuzzy numbers. This integrated approach, which synthesizes these three challenging features, generalizes several existing models in the literature. We address the problem for both type (i)-gH and type (ii)-gH differentiable solutions, deriving two distinct mild solution formulas via Wright-type functions and semigroup theory. The core existence results are established using a sophisticated application of the Schauder and Krasnosel'skii fixed point theorems. A complete illustrative example is provided to demonstrate the practical application of the main theorems. The results presented herein provide a significant extension of the existing theory for both classical and fuzzy fractional differential equations.

کلیدواژه ها:

Fuzzy fractional differential equations ، Caputo fractional derivative ، Mild solution ، Semigroups ، Schauder fixed point theorem ، gH-differentiability