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.

Keywords

Main Subjects


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