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This work is devoted to introducing a full overview of q-calculus and fractional q-calculus. Several theorems, lemmas, corollaries, and results are stated and proved in detail by our methodologies. We think that this work would pave the way to further explore and investigate more results and applications in the field of fractional q-calculus. Furthermore, the presented framework may serve as a foundation for advancing research in related mathematical areas, such as quantum calculus and its various extensions. By leveraging these results, researchers can develop new techniques for solving complex problems.

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On Q-fractional Calculus: Foundations and Theoretical Insights

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  • 发表日期：

    2025年

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  • Iqbal M. Batiha,
  • Sharaf Aldeen O. Albteiha,
  • Shaher Momani

摘要

This work is devoted to introducing a full overview of q-calculus and fractional q-calculus. Several theorems, lemmas, corollaries, and results are stated and proved in detail by our methodologies. We think that this work would pave the way to further explore and investigate more results and applications in the field of fractional q-calculus. Furthermore, the presented framework may serve as a foundation for advancing research in related mathematical areas, such as quantum calculus and its various extensions. By leveraging these results, researchers can develop new techniques for solving complex problems.