Electron. J. Diff. Equ., Vol. 2013 (2013), No. 258, pp. 1-9.

A uniqueness result for an inverse problem in a space-time fractional diffusion equation

Salih Tatar, Suleyman Ulusoy

Abstract:
Fractional (nonlocal) diffusion equations replace the integer-order derivatives in space and time by fractional-order derivatives. This article considers a nonlocal inverse problem and shows that the exponents of the fractional time and space derivatives are determined uniquely by the data $u(t, 0)= g(t),\; 0 < t < T$. The uniqueness result is a theoretical background for determining experimentally the order of many anomalous diffusion phenomena, which are important in physics and in environmental engineering.

Submitted May 8, 2013. Published November 22, 2013.
Math Subject Classifications: 45K05, 35R30, 65M32.
Key Words: Fractional derivative; fractional Laplacian; weak solution; inverse problem; Mittag-Leffler function; Cauchy problem.

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Salih Tatar
Department of Mathematics
Faculty of Education, Zirve University
Sahinbey, Gaziantep, 27270, Turkey
email: salih.tatar@zirve.edu.tr
http://person.zirve.edu.tr/statar/
Süleyman Ulusoy
Department of Mathematics
Faculty of Education, Zirve University
Sahinbey, Gaziantep, 27270, Turkey
email: suleyman.ulusoy@zirve.edu.tr
http://person.zirve.edu.tr/ulusoy/

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