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

Kyeong Hun Kim, Sungbin Lim

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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
Volume53
Issue number4
DOIs
Publication statusPublished - 2016

Fingerprint

Fractional Diffusion
Fundamental Solution
Diffusion equation
Wave equation
Asymptotic Behavior
Riemann-Liouville Fractional Derivative
Subordinator
Derivative
Transition Density
Fractional Integral
Laplace Operator
Partial derivative
Fractional Derivative
Fractional
kernel
Upper bound

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Asymptotic behaviors of fundamental solution and its derivatives to fractional diffusion-wave equations. / Kim, Kyeong Hun; Lim, Sungbin.

In: Journal of the Korean Mathematical Society, Vol. 53, No. 4, 2016, p. 929-967.

Research output: Contribution to journalArticle

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