EXISTENCE, UNIQUENESS, HYERS–ULAM STABILITY AND CONTROLLABILITY RESULTS OF INTEGRO-DIFFERENTIAL EQUATIONS RELATED TO THE FRACTIONAL CAPUTO DERIVATIVE

This study explores the Hyers–Ulam stability and controllability of nonlinear integro-differential equations involving the Caputo fractional derivative. Fixed point methods are employed to establish the existence and uniqueness of solutions. The Hyers–Ulam stability is analyzed within the context of the Caputo fractional operator by formulating the necessary conditions. Furthermore, the controllability of the obtained solutions is investigated, providing a deeper understanding of their qualitative properties. The study also presents illustrative examples and practical applications of the proposed equations.