Asymptotic behaviors of fundamental solution and its derivatives to fractional diffusion-wave equations

Kyeong Hun Kim, Sungbin Lim

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14 Citations (Scopus)


Let p(t; x) be the fundamental solution to the problem (Formula Presented), then the kernel p(t; x) becomes the transition density of a Lévy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t; x) and its space and time fractional derivatives (Formula Presented); where Dn x is a partial derivative of order n with respect to x, (-Δx)γ is a fractional Laplace operator and Dσ t and Iσ t are Riemann-Liouville fractional derivative and integral respectively.

Original languageEnglish
Pages (from-to)929-967
Number of pages39
JournalJournal of the Korean Mathematical Society
Issue number4
Publication statusPublished - 2016



  • Asymptotic behavior
  • Fractional diffusion
  • Fundamental solution
  • Lévy process
  • Space-time fractional differential equation

ASJC Scopus subject areas

  • Mathematics(all)

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