Fractal Riemann-Stieltjes Calculus

Abstract

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. © Diogenes Co.Ltd 2026.