%AZheng, Xiangcheng%ALi, Yiqun%ACheng, Jin%AWang, Hong%Anull Ed.%BJournal Name: Journal of Inverse and Ill-posed Problems; Journal Volume: 29; Journal Issue: 2 %D2021%I %JJournal Name: Journal of Inverse and Ill-posed Problems; Journal Volume: 29; Journal Issue: 2 %K %MOSTI ID: 10295130 %PMedium: X %TInverting the variable fractional order in a variable-order space-fractional diffusion equation with variable diffusivity: analysis and simulation %XAbstract Variable-order space-fractional diffusion equations provide very competitive modeling capabilities of challenging phenomena, including anomalously superdiffusive transport of solutes in heterogeneous porous media, long-range spatial interactions and other applications, as well as eliminating the nonphysical boundary layers of the solutions to their constant-order analogues.In this paper, we prove the uniqueness of determining the variable fractional order of the homogeneous Dirichlet boundary-value problem of the one-sided linear variable-order space-fractional diffusion equation with some observed values of the unknown solutions near the boundary of the spatial domain.We base on the analysis to develop a spectral-Galerkin Levenberg–Marquardt method and a finite difference Levenberg–Marquardt method to numerically invert the variable order.We carry out numerical experiments to investigate the numerical performance of these methods. %0Journal Article