Extensive View for Implicit Second-Order Differential Equations with a Feedback Control

The current research investigates the solvability and stability of implicit second-order differential equations subject to fractional integral boundary conditions under the influence of a fractional control. The analysis is grounded in the application of Krasnoselskii’s fixed point theorem to establish the existence and stability of solutions. To complement the theoretical results, numerical calculations are provided, to validate our findings. Furthermore, detailed comparisons with the existing literature highlight the efficacy and novelty of the proposed approach.