Leibniz-type rule of variable-order fractional derivative and application to build Lie symmetry framework

作者：

Highlights：

• We present a Leibniz-type rule of the variable-order fractional derivative in the sense of Caputo fractional derivative.

• According the Leibniz-type rule, we build a Lie symmetry framework of the variable-order fractional PDEs under the Caputo fractional derivative.

• The symmetry structure of a class of scalar variable-order timefractional PDEs are found.

摘要

•We present a Leibniz-type rule of the variable-order fractional derivative in the sense of Caputo fractional derivative.•According the Leibniz-type rule, we build a Lie symmetry framework of the variable-order fractional PDEs under the Caputo fractional derivative.•The symmetry structure of a class of scalar variable-order timefractional PDEs are found.

论文关键词：Leibniz-type rule,Variable-order fractional derivative,Lie symmetry framework,Symmetry structure,Reduction

论文评审过程：Received 29 October 2021, Revised 1 April 2022, Accepted 17 May 2022, Available online 23 May 2022, Version of Record 23 May 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127268