Author(s)： Yuko Hatano, Junichi Nakagawa, Shengzhang Wang and Masahiro Yamamoto

J. Math-for-Ind. 5A (2013) 51-57.

• File： JMI2013A-7.pdf (153KB)

Abstract
We prove formulae of reconstructing the order of fractional derivative in time in the fractional diffusion equation by time history at one fixed spatial point. The proof is based on asymptotics of the solution as $t \to 0$ or $t \to \infty$. The order is important for evaluating the anomaly of the diffusion in heterogeneous medium, and in particular, the order determines the decay rate of solution for large $t$. We show numerical tests for our reconstruction formula.

Keyword(s).　 fractional diffusion equation, order of fractional derivative, inverse problem, reconstruction formula, error analysis