Implicit Fractional Differential Equation with Time-Varying State-Dependent Feedback

The present article introduces and investigates a class of implicit fractional differential equations with time-varying state-dependent feedback, a setting that significantly extends existing fractional delay models. Existence and uniqueness results are established via the Banach fixed-point theorem, while sharp exponential growth estimates for the solutions are derived using a generalized Gronwall-type inequality. These results provide new analytical insights into the qualitative behavior of fractional systems with dynamically evolving feedback mechanisms.