A High Order Formula to Approximate the Caputo Fractional Derivative

• 作者: F.Mostajeran R.Mokhtari
• 来源期刊: 应用数学与计算数学学报(英文)
• 学科: 数学
• 关键词: Caputo FRACTIONAL DERIVATIVE FRACTIONAL PARTIAL differential equation Finite difference scheme
• 年，卷（期）: 2020,（1）
• 页码范围: 1-29
• 页数: 29页
• 分类号: O17

摘要

We present here a high-order numerical formula for approximating the Caputo fractional derivative of order??for 0<α<1.This new formula is on the basis of the third degree Lagrange interpolating polynomial and may be used as a powerful tool in solving some kinds of fractional ordinary/partial diff erential equations.In comparison with the previous formulae,the main superiority of the new formula is its order of accuracy which is 4?α,while the order of accuracy of the previous ones is less than 3.It must be pointed out that the proposed formula and other existing formulae have almost the same computational cost.The eff ectiveness and the applicability of the proposed formula are investigated by testing three distinct numerical examples.Moreover,an application of the new formula in solving some fractional partial diff erential equations is presented by constructing a fi nite diff erence scheme.A PDE-based image denoising approach is proposed to demonstrate the performance of the proposed scheme.