Artificial boundary condition for a modified fractional diffusion problem

Abeeb A. Awotunde, Ryad Ghanam, Nasser eddine Tatar

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

A diffusion problem involving a time derivative acting on two time scales represented by two fractional derivatives is investigated. The orders of the fractional derivatives are both between 0 and 1 and therefore the problem corresponds to the subdiffusion case. It is considered on a semi-infinite axis and the forcing term and the initial data are assumed compactly supported. To reduce the problem to that support there is a risk of being lead to an ‘infected’ problem due to the reflected waves on the new settled boundary. To avoid this undesirable effect of reflected waves on the standard boundaries, we establish artificial boundaries and find the appropriate artificial boundary conditions. Then, using the properties of fractional derivatives, a generalized version of the Mittag-Leffler function and some adequate manipulations of inverse Laplace transforms we find the explicit solution of the reduced problem.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalBoundary Value Problems
Volume2015
Issue number1
DOIs
Publication statusPublished - 2015

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Artificial Boundary Conditions
Fractional Diffusion
Diffusion Problem
Fractional Derivative
Inverse Laplace Transform
Artificial Boundary
Mittag-Leffler Function
Subdiffusion
Forcing Term
Explicit Solution
Manipulation
Time Scales
Derivative

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis

Cite this

Artificial boundary condition for a modified fractional diffusion problem. / Awotunde, Abeeb A.; Ghanam, Ryad; Tatar, Nasser eddine.

In: Boundary Value Problems, Vol. 2015, No. 1, 2015, p. 1-17.

Research output: Contribution to journalArticle

Awotunde, Abeeb A. ; Ghanam, Ryad ; Tatar, Nasser eddine. / Artificial boundary condition for a modified fractional diffusion problem. In: Boundary Value Problems. 2015 ; Vol. 2015, No. 1. pp. 1-17.
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