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<p>Fractional calculus has been widely applied in various fields due to its ability to describe history and nonlocality. The Caputo derivative is frequently applied in time-fractional partial differential equations. Consequently, its numerical approximation has attracted significant research interest. This paper summarizes several common approximation methods for the Caputo derivative, along with their numerical accuracy and coefficient properties. Numerical experiments are provided to verify the convergence order of these approximations.</p>

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A Study of Several Numerical Approaches for Caputo Derivative

  • 期刊论文

  • 发表日期：

    2026年4月13日

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  • Yitong Chen,
  • Baoting Wang,
  • Min Cai

摘要

Fractional calculus has been widely applied in various fields due to its ability to describe history and nonlocality. The Caputo derivative is frequently applied in time-fractional partial differential equations. Consequently, its numerical approximation has attracted significant research interest. This paper summarizes several common approximation methods for the Caputo derivative, along with their numerical accuracy and coefficient properties. Numerical experiments are provided to verify the convergence order of these approximations.