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<p>A novel high-accuracy numerical approach is presented for Caputo fractional order initial value problems with nonsmooth solutions. Due to the nonsmoothness of solutions, the numerical treatment of such problems is difficult. Firstly, a variable transformation is introduced to transform the original problem to an integral-differential equation with smooth solution. Then a high-accuracy numerical method is proposed for the transformed problem. The present approach is verified by three numerical experiments.</p>

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A novel high-accuracy numerical approach for initial value problems of fractional order with nonsmooth solutions

  • 期刊论文

  • 发表日期：

    2025年3月21日

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  • Xiuying Li,
  • Boying Wu

摘要

A novel high-accuracy numerical approach is presented for Caputo fractional order initial value problems with nonsmooth solutions. Due to the nonsmoothness of solutions, the numerical treatment of such problems is difficult. Firstly, a variable transformation is introduced to transform the original problem to an integral-differential equation with smooth solution. Then a high-accuracy numerical method is proposed for the transformed problem. The present approach is verified by three numerical experiments.