The profile of blowing-up solutions to a nonlinear system of fractional differential equations

Mokhtar Kirane, Salman A. Malik

Research output: Contribution to journalArticlepeer-review

43 Scopus citations

Abstract

We investigate the profile of the blowing-up solutions to the nonlinear nonlocal system (FDS): u′(t)+D0+α(u-u0)(t)=|v(t)|q,t>0, v′(t)+D0+β(v-v0)(t)=|u(t)|p,t>0, where u(0)=u0>0,v(0)=v0>0, p>1,q>1 are given constants and D0+α and D0+β, 0<α<1, 0<β<1, stand for the RiemannLiouville fractional derivatives. Our method of proof relies on comparisons of the solution to the system (FDS) with solutions of the subsystems obtained from the system (FDS) by dropping either the usual derivatives or the fractional derivatives.

Original languageBritish English
Pages (from-to)3723-3736
Number of pages14
JournalNonlinear Analysis, Theory, Methods and Applications
Volume73
Issue number12
DOIs
StatePublished - 15 Dec 2010

Keywords

  • Blow-up time
  • Fractional derivative
  • Integral equations
  • Laplace transform
  • Nonlinear system

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