Abstract
A sufficient condition for the nonexistence of blowing-up mild
solutions of a nonlinear evolution fractional functional-differential equation
associated with a strongly continuous semigroup and with a nonlinearity containing
the Riemann–Liouville fractional integral is established. We prove a result on a new
type of nonlinear integral inequalities with weakly singular kernels and delay and
apply it in the proof of the result on the nonexistence of blowing-up solutions.
This result is applied to a fractionally damped pendulum equation with a time delay
forcing term (a feedback control).