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Title: Inverting the variable fractional order in a variable-order space-fractional diffusion equation with variable diffusivity: analysis and simulation
Abstract 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.
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Award ID(s):
Publication Date:
Journal Name:
Journal of Inverse and Ill-posed Problems
Page Range or eLocation-ID:
219 to 231
Sponsoring Org:
National Science Foundation
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