Analysis of fractional diffusion equations of distributed order: Maximum principles and their applications

Mohammed Al-Refai, Yuri Luchko

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

In this paper, we formulate and prove the weak and strong maximum principles for a general parabolic-type fractional differential operator with the Riemann-Liouville time-fractional derivative of distributed order. The proofs of the maximum principles are based on an estimate of the Riemann-Liouville fractional derivative at its maximum point that was recently derived by the authors. Some a priori norm estimates for solutions to initial-boundary value problems for linear and nonlinear fractional diffusion equations of distributed order and uniqueness results for these problems are presented.

Original languageEnglish
Pages (from-to)123-133
Number of pages11
JournalAnalysis (Germany)
Volume36
Issue number2
DOIs
Publication statusPublished - May 1 2016

Keywords

  • Riemann-Liouville fractional derivative
  • distributed-order time-fractional diffusion equation
  • initial-boundary value problems
  • linear equation of distributed order
  • maximum principle
  • nonlinear equation of distributed order
  • stability
  • uniqueness theorem

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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