In this work,a novel time-stepping L1 formula is developed for a hidden-memory variable-order Caputo’s fractional derivative with an initial singularity.This formula can obtain second-order accuracy and an error esti...In this work,a novel time-stepping L1 formula is developed for a hidden-memory variable-order Caputo’s fractional derivative with an initial singularity.This formula can obtain second-order accuracy and an error estimate is analyzed strictly.As an application,a fully discrete difference scheme is established for the initial-boundary value problem of a hidden-memory variable-order time fractional diffusion model.Numerical experiments are provided to support our theoretical results.展开更多
基金supported by the National Natural Science Foundation of China(No.12201076)the China Postdoctoral Science Foundation(No.2023M732180)。
文摘In this work,a novel time-stepping L1 formula is developed for a hidden-memory variable-order Caputo’s fractional derivative with an initial singularity.This formula can obtain second-order accuracy and an error estimate is analyzed strictly.As an application,a fully discrete difference scheme is established for the initial-boundary value problem of a hidden-memory variable-order time fractional diffusion model.Numerical experiments are provided to support our theoretical results.
