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Articles

Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation

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Pages 570-579 | Received 10 Apr 2014, Accepted 16 May 2014, Published online: 16 Jul 2014

References

  • Metzler R, Klafter J. The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 2000;339:1–77.
  • Luchko Y. Boundary value problems for the generalized time-fractional diffusion equation of distributed order. Fract. Calc. Appl. Anal. 2009;12:409–422.
  • Luchko Y. Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation. J. Math. Anal. Appl. 2011;374:538–548.
  • Podlubny I. Fractional differential equations. San Diego: Academic Press; 1999.
  • Beckers S, Yamamoto M. Regularity and unique existence of solution to linear diffusion equation with multiple time-fractional derivatives. In: Bredies K, Clason C, Kunisch K, von Winckel G, editors. Control and Optimization with PDE Constraints. Basel: Birkhäuser; 2013. p. 45–56.
  • Li Z, Liu Y, Yamamoto M. Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients. 2013. arXiv: 1312.2112.
  • Li Z, Yamamoto M. Initial-boundary value problems for linear diffusion equation with multiple time-fractional derivatives. 2013. arXiv:1306.2778v2.
  • Cheng M, Nakagawa J, Yamamoto M, Yamazaki T. Uniqueness in an inverse problem for a one dimensional fractional diffusion equation. Inverse Probl. 2009;25:115002.
  • Hatano Y, Nakagawa J, Wang S, Yamamoto M. Determination of order in fractional diffusion equation. J. Math-for-Ind. 2013;5A:51–57.
  • Luchko Y, Gorenflo R. An operational method for solving fractional differential equations with the Caputo derivatives. Acta Math. Vietnam. 1999;24:207–233.
  • Li Z, Imanuvilov O, Yamamoto M. Uniqueness in inverse boundary value problems for fractional diffusion equations. 2014. arXiv: 1404.7024.
  • Tanabe H. Equations of evolution. London: Pitman; 1979.
  • Courant R, Hilbert D. Methods of mathematical physics. New York (NY): Interscience Publishers; 1953.

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