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On the nonexistence of blowing-up solutions to a fractional functional-differential equation
-
Mokhtar Kirane
,
Milan Medved'
Published/Copyright:
February 29, 2012
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).
Keywords.: Henry–Gronwall inequality; Riemann–Liouville fractional integral; functional-differential equation; blowing-up solution
Received: 2010-12-30
Revised: 2011-11-27
Published Online: 2012-02-29
Published in Print: 2012-March
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Henry–Gronwall inequality;
Riemann–Liouville fractional integral;
functional-differential equation;
blowing-up solution
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