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

By Hongguang Sun, A. Chang, Yong Zhang, Wen Chen. Fractional Calculus and Applied Analysis, 2019

400 citations recorded by the source corpus.

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.

Subfields: Control and Systems Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f7cf2c30679360dcd6ff45d2b95223cb6f6baf13

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Citations in the corpus

Some further results of the laplace transform for variable–order fractional difference equations (2019, background): “A survey of variable–order fractional differential equation is provided [12].”