Di Teodoro, AntonioGude, Juan JoséCamacho, Oscar2026-11-132026-11-132026-12-01Di Teodoro, A., Gude, J. J., & Camacho, O. (2026). A nested weighted framework for Podlubny-type fractional PID controllers. Chaos, Solitons and Fractals, 213. https://doi.org/10.1016/J.CHAOS.2026.1192170960-077910.1016/J.CHAOS.2026.119217https://hdl.handle.net/20.500.14454/6959This paper presents a unified nested weighted framework for the systematic synthesis of Podlubny-type fractional PID controllers through the constructive generation of generalized fractional operators. The proposed methodology adopts a composition-based perspective in which generalized fractional operators are recursively constructed from weighted differential and integral mappings, allowing classical formulations, including the Riemann–Liouville and Caputo operators, to be recovered as particular cases. Within this framework, a novel pulling-type weighted fractional operator is introduced and its fundamental analytical properties, including linearity, kernel characterization, boundedness, semigroup behavior, and Laplace-domain representation, are rigorously established. These results provide the mathematical foundation for deriving a generalized family of weighted Podlubny-type fractional PID controllers, where the weighting functions become explicit design parameters governing memory distribution and closed-loop dynamics. Consequently, the proposed framework transforms the construction of generalized fractional operators into a systematic methodology for fractional controller synthesis, establishing a constructive link between generalized fractional calculus and fractional-order control design.eng© 2026 The Author(s)Controller synthesisFractional calculusFractional-order controlGeneralized fractional operatorsNested weighted operatorsPID controllersPodlubny-type fractionaljournal article2026-11-13