A Study of Several Numerical Approaches for Caputo Derivative

Abstract

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.

Keywords

Fractional calculus / Caputo derivative / Numerical approximation / 26A33 / 65D25 / 65M06

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