Determination of an unknown source term and the temperature distribution for the linear heat equation involving fractional derivative in time

Mokhtar Kirane, Salman A. Malik

Research output: Contribution to journalArticlepeer-review

83 Scopus citations

Abstract

We consider the inverse problem of finding the temperature distribution and the heat source whenever the temperatures at the initial time and the final time are given. The problem considered is one dimensional and the unknown heat source is supposed to be space dependent only. The existence and uniqueness results are proved.

Original languageBritish English
Pages (from-to)163-170
Number of pages8
JournalApplied Mathematics and Computation
Volume218
Issue number1
DOIs
StatePublished - 1 Sep 2011

Keywords

  • Biorthogonal system of functions
  • Fourier series
  • Fractional derivative
  • Heat equation
  • Integral equations
  • Inverse problem

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