ABSTRACT

We study a numerical reconstruction strategy for the potential in the fractional Calder\'on problem from a single partial exterior measurement. The forward model is the fractional Schrödinger equation in a bounded domain, with prescribed exterior Dirichlet datum and corresponding measurement of the exterior flux in an open observation set. Building on the theoretical foundations of the fractional Calderón problem [T. Ghosh, M. Salo, and G. Uhlmann, 2020], we propose a decomposition strategy and a Galerkin–Tikhonov method to recover the potential through a stabilized least-squares formulation. We establish existence, uniqueness and conditional convergence of the discrete reconstructor with a priori error estimates, and we demonstrate compatibility with practical schemes for the integral fractional Laplacian [G. Acosta and J.P. Borthagaray, 2017]. Numerical experiments in one and two dimensions show stable reconstructions of smooth and discontinuous potentials [M. Dwivedi, J. Railo, and A. Rupp, 2026].