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This chapter outlines the fundamental structure of the Nabla Mittag–Leffler Euler difference scheme for FODEs in the sense of Caputo. Additionally, the fractional PECE algorithm is proposed as an effective solution for this type of implicit difference in numerical calculations. Furthermore, the corresponding nonlocal Nabla difference equations are modelled and the well-posed problem is investigated.

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The Theory of Nabla MLEDs

  • 章节

  • 发表日期：

    2025年

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  • Tianwei Zhang,
  • Yongkun Li,
  • Jianwen Zhou

摘要

This chapter outlines the fundamental structure of the Nabla Mittag–Leffler Euler difference scheme for FODEs in the sense of Caputo. Additionally, the fractional PECE algorithm is proposed as an effective solution for this type of implicit difference in numerical calculations. Furthermore, the corresponding nonlocal Nabla difference equations are modelled and the well-posed problem is investigated.