An introduction to weighted operators via composition and selected properties, aimed at numerical implementation
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Fecha
2025-12
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Elsevier B.V.
Resumen
This work introduces a novel class of weighted fractional operators constructed through the composition of differential and integral operators. In particular, we propose the operator q¯Dxμ, which generalizes classical fractional derivatives while maintaining essential properties such as linearity. Although the semigroup property and the Leibniz rule do not hold in their traditional forms, we derive analogous formulations by combining the proposed operator with the Riemann-Liouville derivative. Furthermore, a numerical representation based on the Grünwald-Letnikov method is developed, enabling efficient discretization and simulation of the weighted operator in cases where analytical solutions are intractable. The approach also considers the interplay between Laplace transforms and convolutions, which is crucial for real-world applications in control and signal processing.
Palabras clave
Composition properties
Fractional PID control
Fractional systems
Industrial Process Control
Weighted Operators
Fractional PID control
Fractional systems
Industrial Process Control
Weighted Operators
Descripción
Ponencia presentada en la 3th IFAC Conference on Fractional Differentiation and its Applications ICFDA 2025, celebrada en Argelia entre el 16 y el 18 de diciembre de 2025
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Cita
Camacho, O., Chalco, R., Di Teodoro, A., Gude, J. J., Montaluisa, R., Vargas, C., Vega, S., & Villegas, M. (2025). An introduction to weighted operators via composition and selected properties, aimed at numerical implementation. IFAC-PapersOnLine, 59(37), 47-52. https://doi.org/10.1016/J.IFACOL.2026.01.009