Existence, Uniqueness of Multi-time scale Stochastic Fractional Neural Networks with Time Delay

This manuscript presents a systematic study on stochastic fractional neural networks with time delay, focusing on the establishment of existence and uniqueness of solutions in the phase space M^2([-,T];R^n). Using the Picard iteration method, explicit sufficient conditions guaranteeing the well-posedness of the system are rigorously established. A key contribution of this work is the derivation of analytical upper bounds for the Picard approximation sequence, which provides insight into the convergence behavior and reliability of the obtained solutions. Numerical examples are presented to confirm the theoretical findings and demonstrate the effectiveness of the proposed approach.