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

Laguerre Functions and Their Applications to Tempered Fractional Differential Equations on... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Scientific Computing Springer Journals

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

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Algorithms; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theoretical, Mathematical and Computational Physics
ISSN
0885-7474
eISSN
1573-7691
D.O.I.
10.1007/s10915-017-0495-7
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Scientific ComputingSpringer Journals

Published: Jul 18, 2017

References

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