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<p>In this article, we give a short summary of fractal variation in calculus, deriving both the general form of the fractal Euler equation and another version. Moreover, we present a double integral calculus of variations, which encompasses the classical calculus of variations for two variables as specific instances. Our study also explores fractal double integrals over standard regions, thus establishing the fundamental theorem of fractal double integrals.</p>

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Double fractal integral calculus of variations

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Gülizar Gülenay Zengin,
  • Hemanta Kalita,
  • Santosh Kumar,
  • Palle E. T. Jorgensen

摘要

In this article, we give a short summary of fractal variation in calculus, deriving both the general form of the fractal Euler equation and another version. Moreover, we present a double integral calculus of variations, which encompasses the classical calculus of variations for two variables as specific instances. Our study also explores fractal double integrals over standard regions, thus establishing the fundamental theorem of fractal double integrals.