A Concise Review on the Numerical Treatment of Generalized Fractional Equations

Xuhao Li and Patricia J. Y. Wong ()
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Xuhao Li: School of Mathematical Sciences, Anhui University, Jiulong Road, Hefei 230601, China
Patricia J. Y. Wong: School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

Mathematics, 2025, vol. 13, issue 22, 1-28

Abstract: In this paper, we shall give a concise review of recent numerical methods of some generalized fractional models. As is elucidated later, the generalized fractional models may arise from either mathematical point of view or application point of view. We shall focus on the former one and discuss the numerical methods for these models in a concise manner. Finally, some potential research directions are proposed based on existing results as well as some advanced new topics. We hope this review can provide a sketch of current and future studies of generalized fractional models for interested readers.

Keywords: generalized fractional model; time-diffusion problem; generalized interpolation; generalized convolution quadrature (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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