An inverse source problem for a two dimensional time fractional diffusion equation with nonlocal boundary conditions

Mokhtar Kirane, Salman A. Malik, Mohammed A. Al-Gwaiz

Research output: Contribution to journalArticlepeer-review

107 Scopus citations

Abstract

We consider the inverse source problem for a time fractional diffusion equation. The unknown source term is independent of the time variable, and the problem is considered in two dimensions. A biorthogonal system of functions consisting of two Riesz bases of the space L2[(0,1) × (0,1)], obtained from eigenfunctions and associated functions of the spectral problem and its adjoint problem, is used to represent the solution of the inverse problem. Using the properties of the biorthogonal system of functions, we show the existence and uniqueness of the solution of the inverse problem and its continuous dependence on the data.

Original languageBritish English
Pages (from-to)1056-1069
Number of pages14
JournalMathematical Methods in the Applied Sciences
Volume36
Issue number9
DOIs
StatePublished - Jun 2013

Keywords

  • biorthogonal system of functions
  • diffusion equation
  • Fourier series
  • fractional derivative
  • integral equations
  • inverse problem

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