Maximum principle for certain generalized time and space fractional diffusion equations

Ahmed Alsaedi, Bashir Ahmad, Mokhtar Kirane

Research output: Contribution to journalArticlepeer-review

55 Scopus citations

Abstract

We present an inequality for fractional derivatives related to the Leibniz rule that not only answers positively a conjecture raised by J. I. Diaz, T. Pierantozi, and L. Vzquez but also helps us to obtain a modern proof of the maximum principle for fractional differential equations. The inequality turns out to be versatile in nature as it can be used to obtain a priori estimates for many fractional differential problems.

Original languageBritish English
Pages (from-to)163-175
Number of pages13
JournalQuarterly of Applied Mathematics
Volume73
Issue number1
DOIs
StatePublished - 2015

Keywords

  • Fractional porous medium equation
  • Maximum principle
  • Time and space fractional differential equation
  • Time fractional differential equation

Fingerprint

Dive into the research topics of 'Maximum principle for certain generalized time and space fractional diffusion equations'. Together they form a unique fingerprint.

Cite this