Laguerre functions and their applications to tempered fractional differential equations on infinite intervals

• Main Authors: Chen, Sheng, Shen, Jie, Wang, Li-Lian
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2020
• Subjects: Science::Mathematics; Tempered Fractional Differential Equations; Singularity
• Online Access: https://hdl.handle.net/10356/139550
• Institution: Nanyang Technological University

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.