On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source Function

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ÖZKUM G., DEMİR A., Erman S., Korkmaz E., Ozgur B.

ADVANCES IN MATHEMATICAL PHYSICS, vol.2013, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2013
  • Publication Date: 2013
  • Doi Number: 10.1155/2013/476154
  • Journal Name: ADVANCES IN MATHEMATICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Kocaeli University Affiliated: Yes

Abstract

The study in this paper mainly concerns the inverse problem of determining an unknown source function in the linear fractional differential equation with variable coefficient using Adomian decomposition method (ADM). We apply ADM to determine the continuous right hand side functions.. f(x) and f(t) in the heat-like diffusion equations D(t)(alpha)u(x, t) = h (x)u(xx)(x, t) +f(x) and f(x) (..,..) = h (x)u(xx)(x, t) + f(t), respectively. The results reveal that ADM is very effective and simple for the inverse problem of determining the source function.