Fractal Riemann-Stieltjes Calculus

Khalili Golmankhaneh A., Castillo R. E., Zayed A. I., Jørgensen P. E. T.

Fractional Calculus and Applied Analysis, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1007/s13540-025-00468-4
  • Dergi Adı: Fractional Calculus and Applied Analysis
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: Fractal Calculus, Fractal Fundamental Theorem of Calculus, Fractal mean value theorem, Fractal Riemann-Stieltjes Integral
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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 Fϕ(x)α-differentiable functions. Examples are provided and illustrated through plots to highlight the details of these concepts.