Jornet, MarcNieto Roig, Juan José2026-03-242026-03-242024-10-29Jornet, M., & Nieto, J. J. (2025). Representation and inequalities involving continuous linear functionals and fractional derivatives. Advances in Operator Theory, 10(1). https://doi.org/10.1007/S43036-024-00397-8https://hdl.handle.net/10347/46490We investigate how continuous linear functionals can be represented in terms of generic operators and certain kernels (Peano kernels), and we study lower bounds for the operators as a consequence, in the space of square-integrable functions. We apply and develop the theory for the Riemann–Liouville fractional derivative (an inverse of the Riemann–Liouville integral), where inequalities are derived with the Gaussian hypergeometric function. This work is inspired by the recent contributions by Fernandez and Buranay (J Comput Appl Math 441:115705, 2024) and Jornet (Arch Math, 2024).eng© The Author(s) 2024Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Representation of functionalsInequalitiesDifferintegral operatorsRiemann-Liouville fractional calculusjournal article2025-12-0410.1007/S43036-024-00397-82538-225Xopen access2538-225X