Golmankhaneh, Alireza KhaliliRodriguez-Lopez, RosanaStamova, Ivanka M.Celik, Ercan2025-07-302025-07-3020252345-394X2382-986910.22124/jmm.2025.29566.26292-s2.0-105010723585https://doi.org/10.22124/jmm.2025.29566.2629In this paper, we begin by providing a concise overview of fractal calculus. We then explore the concepts of fractal complex numbers and functions, define the fractal complex derivative, and derive the fractal Cauchy-Riemann equations. Additionally, we introduce fractal contour integrals, offer illustrative examples, and present their visualizations. Finally, we examine and visualize the transformations of circles under fractal complex functions.eninfo:eu-repo/semantics/closedAccessFractal CalculusFractal Complex NumberFractal Complex FunctionFractal Complex DerivativeFractal Contour IntegralsArticle133N/AQ4675684WOS:001546030000012