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 RiemannLiouville 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).
Original language | British English |
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Pages (from-to) | 127-144 |
Number of pages | 18 |
Journal | Georgian Mathematical Journal |
Volume | 19 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2012 |
Keywords
- Blowing-up solution
- Functional-differential equation
- HenryGronwall inequality
- RiemannLiouville fractional integral