On the nonexistence of blowing-up solutions to a fractional functional-differential equation

Mokhtar Kirane, Milan Medved', Nasser Eddine Tatar

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

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 languageBritish English
Pages (from-to)127-144
Number of pages18
JournalGeorgian Mathematical Journal
Volume19
Issue number1
DOIs
StatePublished - Mar 2012

Keywords

  • Blowing-up solution
  • Functional-differential equation
  • HenryGronwall inequality
  • RiemannLiouville fractional integral

Fingerprint

Dive into the research topics of 'On the nonexistence of blowing-up solutions to a fractional functional-differential equation'. Together they form a unique fingerprint.

Cite this