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This chapter offers an overview of discrete fractional calculus approaches frequently applied in the analysis of dynamical systems. The focus is primarily on the Caputo and Riemann–Liouville operators, while also addressing other widely used formulations such as the h-fractional operator, the Grunwald-type operator, and the variable-order operator, all of which have broad applications in scientific and engineering fields. Numerous properties are given. Additionally, attention is given to numerical solution technique and the analysis of system stability of the Caputo fractional difference systems.

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Overview of Discrete Fractional Calculus

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  • 发表日期：

    2026年

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  • Amina Aicha Khennaoui,
  • Adel Ouannas,
  • Omar Naifar,
  • Abdellatif Ben Makhlouf

摘要

This chapter offers an overview of discrete fractional calculus approaches frequently applied in the analysis of dynamical systems. The focus is primarily on the Caputo and Riemann–Liouville operators, while also addressing other widely used formulations such as the h-fractional operator, the Grunwald-type operator, and the variable-order operator, all of which have broad applications in scientific and engineering fields. Numerous properties are given. Additionally, attention is given to numerical solution technique and the analysis of system stability of the Caputo fractional difference systems.