DETERMINATION OF TIME DEPENDENT DIFFUSION COEFFICIENT IN TIME FRACTIONAL DIFFUSION EQUATIONS BY FRACTIONAL SCALING TRANSFORMATIONS METHOD


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BAYRAK M. A. , DEMİR A.

BULLETIN OF THE INSTITUTE OF MATHEMATICS ACADEMIA SINICA NEW SERIES, vol.16, no.4, pp.303-319, 2021 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.21915/bimas.2021402
  • Journal Name: BULLETIN OF THE INSTITUTE OF MATHEMATICS ACADEMIA SINICA NEW SERIES
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.303-319
  • Keywords: Time fractional diffusion equation, fractional scaling transformations method, modified Riemann-Liouville fractional derivative, Inverse problem, PARTIAL-DIFFERENTIAL-EQUATIONS, SERIES
  • Kocaeli University Affiliated: Yes

Abstract

This study is devoted to investigation of inverse problem of identifying unknown time-dependent diffusion coefficient in time fractional diffusion equation in the sense of the modified Riemann-Liouville fractional derivative, by employing fractional scaling transformations method. By means of this method fractional order derivatives turns into integer order derivatives which allows us to deal with the easier problem. After establishing the solution and unknown coefficient of integer order diffusion problem, by utilizing the inverse transformation, we construct the solution and unknown coefficient of time fractional diffusion problem. Presented examples illustrate that identified unknown coefficient and the solution of the problem are in a high agreement with the exact solution of the corresponding the inverse problem.