<p>In this paper, we establish the existence and continuous dependence of solutions with respect to the order of the Caputo-Hadamard fractional derivative operator. The novelty of this work lies in applying the Caputo-Hadamard approach to feedback control systems and in employing the relative topological degree for multivalued condensing operators with respect to a measure of noncompactness - a method rarely used because of its abstract nature. Several illustrative examples are provided to highlight the abstract results and to demonstrate the flexibility gained when the solution space is chosen in a general setting rather than being restricted to the real line.</p>