Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 258, pp. 1-9.
Title: A uniqueness result for an inverse problem in a space-time fractional
diffusion equation
Authors: Salih Tatar (Zirve Univ., Sahinbey, Gaziantep, Turkey)
Suleyman Ulusoy (Zirve Univ., Sahinbey, Gaziantep, Turkey)
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.