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math.NA2016★ 48 cited
A Petrov-Galerkin Spectral Element Method for Fractional Elliptic Problems
Ehsan Kharazmi, Mohsen Zayernouri, George Em Karniadakis
We develop a new -continuous Petrov-Galerkin spectral element method for one-dimensional fractional elliptic problems of the form ${}_{0}{\mathcal{D}}_{x}^α u(x) - λu(x) =…
math.NA2016
Petrov-Galerkin and Spectral Collocation Methods for distributed Order Differential Equations
Ehsan Kharazmi, Mohsen Zayernouri, George Em Karniadakis
Distributed order fractional operators offer a rigorous tool for mathematical modelling of multi-physics phenomena, where the differential orders are distributed over a range of va…