Corrigendum to “Neglecting nonlocality leads to unreliable numerical methods for fractional differential equations” [Commun. Nonlinear Sci. Numer. Simulat. 70 (2019) 302–306]

2019 ◽  
Vol 76 ◽  
pp. 138-139 ◽  
Author(s):  
Roberto Garrappa
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Differential

scholarly journals A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications

2019 ◽  
Vol 22 (1) ◽  
pp. 27-59 ◽  
Author(s):  
HongGuang Sun ◽  
Ailian Chang ◽  
Yong Zhang ◽  
Wen Chen
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Relevant Literature ◽  
Physical Models ◽  
Variable Order ◽  
Mathematical Tool ◽  
Fractional Differential ◽  
Mathematical Foundations ◽  
Selection Of

Abstract Variable-order (VO) fractional differential equations (FDEs) with a time (t), space (x) or other variables dependent order have been successfully applied to investigate time and/or space dependent dynamics. This study aims to provide a survey of the recent relevant literature and findings in primary definitions, models, numerical methods and their applications. This review first offers an overview over the existing definitions proposed from different physical and application backgrounds, and then reviews several widely used numerical schemes in simulation. Moreover, as a powerful mathematical tool, the VO-FDE models have been remarkably acknowledged as an alternative and precise approach in effectively describing real-world phenomena. Hereby, we also make a brief summary on different physical models and typical applications. This review is expected to help the readers for the selection of appropriate definition, model and numerical method to solve specific physical and engineering problems.

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