Blowing-up solutions to systems of fractional differential and integral equations with exponential non-linearities

A. Kadem, M. Kirane, C. M. Kirk*, W Edward Olmstead

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We consider two separate systems of fractional differential equations with exponential non-linearities. We also consider the corresponding systems of non-linear Volterra integral equations. We present results on the non-existence of global solutions for each system. Bounds on the blow-up time for each system are provided along with the asymptotic growth near blow-up. Each system can be regarded as a model for the interaction of two weakly diffusive media subjected to Arrhenius-type reactions. Our results indicate that a thermal blow-up cannot be avoided under such conditions.

Original languageEnglish (US)
Pages (from-to)1077-1088
Number of pages12
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume79
Issue number6
DOIs
StatePublished - Aug 5 2014

Keywords

  • anomalous diffusion
  • blow-up
  • fractional differential and integral equations
  • nonlinear Volterra equation

ASJC Scopus subject areas

  • Applied Mathematics

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