|本期目录/Table of Contents|

[1]胡小兰,梁宗旗.带有广义记忆核Caputo分数阶导数的一种新数值离散格式[J].集美大学学报(自然科学版),2025,(1):88-94.
　HU Xiaolan,LIANG Zongqi.A New Numerical Discrete Scheme of Caputo Fractional Derivative with Generalized Memory Kernel[J].Journal of Jimei University,2025,(1):88-94.
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《集美大学学报（自然科学版）》[ISSN:1007-7405/CN:35-1186/N]

卷:
期数:
2025年第1期
页码:
88-94
栏目:
数理科学与信息工程
出版日期:
2025-01-23

文章信息/Info

Title:
A New Numerical Discrete Scheme of Caputo Fractional Derivative with Generalized Memory Kernel
作者:
胡小兰; 梁宗旗
集美大学理学院,福建 厦门 361021
Author(s):
HU Xiaolan; LIANG Zongqi
School of Science,Jimei University,Xiamen 361021,China)
关键词:
Caputo分数阶导数; L1插值; 降阶法; 收敛阶
Keywords:
Caputo-fractional derivative; L1 interpolation; order reduction method; convergence order
分类号:
-
DOI:
-
文献标志码:
A
摘要:
本文主要研究了带有广义记忆核Caputo型分数阶导数的L1差分格式。利用L1线性插值和降阶法构造了带有广义记忆核α（1＜α＜2）阶Caputo型分数阶导数的离散格式,研究了其系数性质,并给出了其截断误差,收敛阶为O（τ3-α）。最后，通过数值算例验证了该格式的有效性和数值精度。
Abstract:
The L1 difference scheme of Caputo-fractional derivative with the generalized memory kernel is proposed in this paper.By the linear interpolation and reduced order method,the discrete numerical scheme of Caputo-fractional derivative with the generalized memory kernel α（1＜α＜2）,namely L1 numerical scheme,is presented,and the nature of the coefficients is also proved.Additionally,an error estimate of numerical scheme is provided,demonstrating that the convergence order is O(τ3-α),where τ and α∈(1,2) are the time step size and the fractional order,respectively.The numerical example is presented to demonstrate the effectiveness of the proposed method and the numerical accuracy is validated.

参考文献/References:

相似文献/References:

[1]杜瑞连,梁宗旗.右侧Caputo分数阶导数的L2－1插值逼近[J].集美大学学报(自然科学版),2017,22(4):68.
　DU Ruilian,LIANG Zongqi.Interpolation Approximation of the Right Side of the Caputo Fractional Derivative[J].Journal of Jimei University,2017,22(1):68.
[2]闫羽媛,梁宗旗.α阶右侧Caputo分数阶导数的高阶插值逼近[J].集美大学学报(自然科学版),2021,26(4):365.
　YAN Yuyuan,LIANG Zongqi.The Higher-Order Interpolation Approximation of the Right Side of Caputo Fractional Derivative[J].Journal of Jimei University,2021,26(1):365.

备注/Memo

备注/Memo:
更新日期/Last Update: 2025-03-10