Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds

作者：

Highlights：

• The general fractional derivatives with memory effects named GC/GRL derivative are proposed.

• The definition of new derivatives is derived from some basic principles.

• The Gurtin–Pipkin theory of heat conduction is reformulated by the GC/GRL derivative.

• Simple numerical schemas for the corresponding FDEs are given.

摘要

•The general fractional derivatives with memory effects named GC/GRL derivative are proposed.•The definition of new derivatives is derived from some basic principles.•The Gurtin–Pipkin theory of heat conduction is reformulated by the GC/GRL derivative.•Simple numerical schemas for the corresponding FDEs are given.

论文关键词：General fractional derivative,Memory effect,Heat conduction,Heat waves,GC derivative,GRL derivative

论文评审过程：Received 28 May 2018, Revised 11 September 2018, Accepted 15 October 2018, Available online 6 November 2018, Version of Record 6 November 2018.

论文官网地址：https://doi.org/10.1016/j.amc.2018.10.037