Analysis of the fractional diffusion equations with fractional derivative of non-singular kernel

Mohammed Al-Refai, Thabet Abdeljawad

Research output: Contribution to journalArticlepeer-review

60 Citations (Scopus)

Abstract

In this paper we study linear and nonlinear fractional diffusion equations with the Caputo fractional derivative of non-singular kernel that has been launched recently (Caputo and Fabrizio in Prog. Fract. Differ. Appl. 1(2):73-85, 2015). We first derive simple and strong maximum principles for the linear fractional equation. We then implement these principles to establish uniqueness and stability results for the linear and nonlinear fractional diffusion problems and to obtain a norm estimate of the solution. In contrast with the previous results of the fractional diffusion equations, the obtained maximum principles are analogous to the ones with the Caputo fractional derivative; however, extra necessary conditions for the existence of a solution of the linear and nonlinear fractional diffusion models are imposed. These conditions affect the norm estimate of the solution as well.

Original languageEnglish
Article number315
JournalAdvances in Difference Equations
Volume2017
Issue number1
DOIs
Publication statusPublished - Dec 1 2017

Keywords

  • fractional derivatives
  • fractional diffusion equations
  • maximum principle

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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