A new lower bound for the $$\textrm{L}^2$$-norm of the Caputo fractional derivative

Abstract

We prove a novel, tight lower bound for the norm in $$\textrm{L}^2[0,T]$$ L 2 [ 0 , T ] of the Caputo fractional derivative. It is based on continuous linear functionals, Peano kernels, and the Gaussian hypergeometric function.