Abstract
In this article we consider an inverse boundary problem, in which the unknown boundary function is to be determined from overposed data in a time-fractional diffusion equation. Based upon the free space fundamental solution, we derive a representation for the solution f as a nonlinear Volterra integral equation of second kind with a weakly singular kernel. Uniqueness and reconstructibility by iteration is an immediate result of a priori assumption on f and applying the fixed point theorem. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method.
Acknowledgements
The authors acknowledge partial support from National Science Foundation grants DMS-0715060 and DMS-0900889 and Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).