1$\sim$2 阶 Caputo 分数阶导数的稳定化数值微分

Abstract

Abstract:

In this paper, a class of regularization methods for solving the 1st to 2nd order Caputo fractional derivatives with perturbation data is proposed based on Lavrentiev regularization idea. Then, under a priori assumptions on the exact data, the convergence rates of the regularized fractional derivatives are proved for both a priori and a posteriori parameter choice strategies.Finally, a numerical calculation scheme for regularized fractional derivatives is designed using the numerical integration rule, and the effectiveness and stability of the numerical calculation scheme are verified through numerical examples.

Key words: numerical differentiation, caputo fractional derivative, regularization, convergence rate.

CLC Number:

O241.4

Jie Zhou, Zhousheng Ruan, Zhenzhen Xie, Junjie Zhu. Stable Numerical Differentiation for the Caputo Fractional OrderDerivatives of Order between 1 and 2[J].Acta mathematica scientia,Series A, 2026, 46(6): 2277-2290.

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References 14

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Stable Numerical Differentiation for the Caputo Fractional OrderDerivatives of Order between 1 and 2

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