Exact controllability of generalized conformable integrodifferential system via contraction mapping theorem

The present work addresses the exact controllability problem of integrodifferential systems involving generalized conformable derivatives. The necessary and sufficient conditions of exact controllability for generalized conformable control linear systems are obtained. By assuming that this corresponding part is exactly controllable, a set of sufficient conditions is provided to guarantee the exact controllability of the semilinear integrodifferential systems. Our results are established by using some advanced mathematical techniques, such as general functional theory, fractional calculus, and the contraction mapping Theorem. The practical relevance and effectiveness of the proposed approach are validated through two illustrative examples that bridge theoretical controllability conditions to practical system analysis.