Scholarlink

<p>In this paper, we provide an overview of fractal calculus, extending the Riemann-Stieltjes calculus to functions supported on fractal sets. We define fractal derivatives of functions with respect to other fractal functions and discuss their properties. Additionally, we present the fractal mean value theorem, including its maximum and minimum values. The fundamental theorem of calculus is demonstrated within this fractal context, establishing the relationship between integrals and derivatives for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( F^{\alpha }_{\phi (x)} \)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>F</mi> <mrow> <mi>ϕ</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mi>α</mi> </msubsup> </math></EquationSource> </InlineEquation>-differentiable functions. Examples are provided and illustrated through plots to highlight the details of these concepts.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Fractal Riemann-Stieltjes Calculus

  • 期刊论文

  • 发表日期：

    2026年2月17日

查看全文
  • Alireza Khalili Golmankhaneh,
  • René Erlín Castillo,
  • Ahmed I. Zayed,
  • Palle E. T. Jørgensen

摘要

In this paper, we provide an overview of fractal calculus, extending the Riemann-Stieltjes calculus to functions supported on fractal sets. We define fractal derivatives of functions with respect to other fractal functions and discuss their properties. Additionally, we present the fractal mean value theorem, including its maximum and minimum values. The fundamental theorem of calculus is demonstrated within this fractal context, establishing the relationship between integrals and derivatives for \( F^{\alpha }_{\phi (x)} \) F ϕ ( x ) α -differentiable functions. Examples are provided and illustrated through plots to highlight the details of these concepts.