This paper starts by investigating the boundedness conditions of the L2-norm of the impulse response of Davidson- Cole type fractional filters cascaded with pure fractional inte- grators. Then, it extends these boundedness conditions to the Lp-norms, with 1 ≤ p ≤ ∞. An illustrative example is then presented. It allows evaluating the integral squared error of a CRONE control loop and compares it to a classical proportional- derivative controller on a parameter varying system.