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Journal of Scientific Computing

Erschienen in:

18.07.2017

Laguerre Functions and Their Applications to Tempered Fractional Differential Equations on Infinite Intervals

verfasst von: Sheng Chen, Jie Shen, Li-Lian Wang

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2018

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Abstract

Tempered fractional diffusion equations (TFDEs) involving tempered fractional derivatives on the whole space were first introduced in Sabzikar et al. (J Comput Phys 293:14–28, 2015), but only the finite-difference approximation to a truncated problem on a finite interval was proposed therein. In this paper, we rigorously show the well-posedness of the models in Sabzikar et al. (2015), and tackle them directly in infinite domains by using generalized Laguerre functions (GLFs) as basis functions. We define a family of GLFs and derive some useful formulas of tempered fractional integrals/derivatives. Moreover, we establish the related GLF-approximation results. In addition, we provide ample numerical evidences to demonstrate the efficiency and “tempered” effect of the underlying solutions of TFDEs.

Vorheriger Artikel Locally Conservative Continuous Galerkin FEM for Pressure Equation in Two-Phase Flow Model in Subsurfaces

Nächster Artikel A Homotopy Method for Parameter Estimation of Nonlinear Differential Equations with Multiple Optima

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Titel: Laguerre Functions and Their Applications to Tempered Fractional Differential Equations on Infinite Intervals
verfasst von: Sheng Chen
Jie Shen
Li-Lian Wang
Publikationsdatum: 18.07.2017
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2018
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0495-7

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