# Simultaneous inversion of the fractional order and the space-dependent source term for the time-fractional diffusion equation

Simultaneous inversion of the fractional order and the space-dependent source term for the... In this paper, a simultaneous identification problem of the spacewise source term and the fractional order for a time-fractional diffusion equation is considered. Firstly, under some assumption and with two different kinds of observation data for one-dimensional and two-dimensional time-fractional diffusion equation, the unique results of the inverse problem are proven by the Laplace transformation method and analytic continuation technique. Then the inverse problems are transformed into Tikhonov type optimization problems, the existence of optimal solutions to the Tikhonov functional is proven. Finally, we adopt an alternating minimization algorithm to solve the optimization problems. The efficiency and stability of the inversion algorithm are tested by several one- and two-dimensional examples. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

# Simultaneous inversion of the fractional order and the space-dependent source term for the time-fractional diffusion equation

Applied Mathematics and Computation, Volume 328 – Jul 1, 2018
15 pages

/lp/elsevier/simultaneous-inversion-of-the-fractional-order-and-the-space-dependent-bXomhJybsp
Publisher
Elsevier
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.01.025
Publisher site
See Article on Publisher Site

### Abstract

In this paper, a simultaneous identification problem of the spacewise source term and the fractional order for a time-fractional diffusion equation is considered. Firstly, under some assumption and with two different kinds of observation data for one-dimensional and two-dimensional time-fractional diffusion equation, the unique results of the inverse problem are proven by the Laplace transformation method and analytic continuation technique. Then the inverse problems are transformed into Tikhonov type optimization problems, the existence of optimal solutions to the Tikhonov functional is proven. Finally, we adopt an alternating minimization algorithm to solve the optimization problems. The efficiency and stability of the inversion algorithm are tested by several one- and two-dimensional examples.

### Journal

Applied Mathematics and ComputationElsevier

Published: Jul 1, 2018

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