Sharp error estimate for fractional Volterra integro-differential equations with delay

ZHENG Weishan

doi:10.13471/j.cnki.acta.snus.2022A077

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Sharp error estimate for fractional Volterra integro-differential equations with delay

Research articles | 更新时间：2023-12-08

- Sharp error estimate for fractional Volterra integro-differential equations with delay
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 62, Issue 6, Pages: 152-158(2023)
- 作者机构：
  
  韩山师范学院数学与统计学院，广东潮州521041
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2022A077
  CLC： O241.8
- Published：25 November 2023，
  
  Published Online：26 September 2023，
  
  Received：06 September 2022，
  
  Accepted：16 December 2022
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郑伟珊.一类时滞分数阶Volterra微积分方程组的严格误差分析[J].中山大学学报(自然科学版),2023,62(06):152-158.

ZHENG Weishan.Sharp error estimate for fractional Volterra integro-differential equations with delay[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(06):152-158.
郑伟珊.一类时滞分数阶Volterra微积分方程组的严格误差分析[J].中山大学学报(自然科学版),2023,62(06):152-158. DOI： 10.13471/j.cnki.acta.snus.2022A077.

ZHENG Weishan.Sharp error estimate for fractional Volterra integro-differential equations with delay[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(06):152-158. DOI： 10.13471/j.cnki.acta.snus.2022A077.

摘要

采用谱配置方法分析带一般时滞项的分数阶Volterra微积分方程. 通过严格的误差分析证明了近似解的误差和近似分数阶导数的误差在

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3.04800010

2.53999996

和

</mo><mo>-</mo><mi>μ</mi></mrow></msup></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></math>

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6.51933336

3.47133350

模意义下呈指数衰减. 最后用数值例子来验证理论分析的正确性.

Abstract

Spectral methods are developed for solving fractional differential equations with vanishing delay numerically. Sharp error estimates are carried out， which indicates that the error of solution and the error of exact fractional derivative decay exponentially in both

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3.04800010

2.53999996

and

</mo><mo>-</mo><mi>μ</mi></mrow></msup></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></math>

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6.01133299

3.47133350

. In the end， a numerical example is presented to confirm our theoretical findings.

关键词

分数阶Volterra微积分方程Jacobi配置法时滞误差估计

Keywords

fractional Volterra integro-differential equationJacobi collocation methoddelaysharp error estimate

references

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GU Z， 2016. Multi-step Chebyshev spectral collocation method for Volterra integro-differential equations［J］. Calcolo， 53（4）： 559-583.

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NEVAI P， 1984. Mean convergence of Lagrange interpolation. III［J］. Trans Amer Math Soc， 282（2）： 669-698.

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SHAH K， JARAD F， ABDELJAWAD T， 2020. On a nonlinear fractional order model of dengue fever disease under Caputo-Fabrizio derivative［J］. Alex Eng J， 59（4）： 2305-2313.

TANG T， XU X， CHENG J， 2008. On spectral methods for Volterra integral equations and the convergence analysis［J］. J Comput Math， 26（6）： 825-837.

TOHIDI E， NAVID SAMADI O R， SHATEYI S， 2014. Convergence analysis of Legendre pseudospectral scheme for solving nonlinear systems of Volterra integral equations［J］. Adv Math Phys， 2014： 1-12.

WEI Y， CHEN Y， 2012. Convergence analysis of the spectral methods for weakly singular Volterra integro-differential equations with smooth solutions［J］. Adv Appl Math Mech， 4（1）： 1-20.

YANG Y， CHEN Y， HUANG Y， 2014. Convergence analysis of the Jacobi spectral-collocation method for fractional integro-differential equations［J］. Acta Math Sci， 34（3）： 673-690.

ZENG F， LIU F， LI C， et al， 2014. A Crank-Nicolson ADI spectral method for a two-dimensional Riesz space fractional nonlinear reaction-diffusion equation［J］. SIAM J Numer Anal， 52（6）： 2599-2622.

ZHANG R， ZHU B， XIE H， 2013. Spectral methods for weakly singular Volterra integral equations with pantograph delays［J］. Front Math China， 8（2）： 281-299.

ZHENG W S， 2021. Jacobi convergence analysis for delay Volterra integral equation with weak singularity［J］. Math Numer Sin， 43（2）： 253-260.

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