My Master’s thesis aimed to develop a theoretical and practical framework for modeling and controlling fractional-order systems within the context of linear control theory. From fractional calculus, I introduced operators capable of describing system dynamics with memory and hereditary effects, extending the classical notion of differentiation to non-integer orders. From linear systems theory, I recovered stability and frequency-domain analysis tools to characterize the behavior of fractional-order transfer functions and to construct equivalent representations for infinite-dimensional systems. From control engineering, I designed and tuned fractional-order controllers, such as PIλ and PDμ, demonstrating their ability to improve robustness, noise filtering, and performance compared to conventional integer-order schemes. Moreover, the integration of fractional modeling and control revealed new insights into the organization of dynamic behavior across scales and provided a foundation for implementing fractional controllers in practical systems, such as power converters.