Fractal complex analysis

Document Type : Research Article

Authors

1 Department of Physics, Ur.C., Islamic Azad University, Urmia 63896, West Azerbaijan, Iran, & Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080-Campus, Van, Turkey

2 Departamento de Estatística, Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, 10587, Spain

3 Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA

4 Department of Applied Mathematics and Informatics, Kyrgyz-Turkish Manas University, Bishkek, Kyrgyzstan

Abstract

In 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.  dditionally, 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.

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Journal of Mathematical Modeling
Volume 13, Issue 3
July 2025
Pages 675-684

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