A short introduction to local fractional complex analysis

TL;DR

This paper introduces foundational concepts in local fractional complex analysis, including integral formulas, series expansions, and residue theorems within complex fractal spaces, expanding classical analysis into fractal contexts.

Contribution

It develops generalized local fractional integral formulas, series, and residue theorems, extending complex analysis to fractal spaces with fractional calculus.

Findings

Derived local fractional complex integral formulas

Established Yang-Taylor and Laurent series in fractal space

Proved generalized residue theorems for fractional complex functions

Abstract

This paper presents a short introduction to local fractional complex analysis. The generalized local fractional complex integral formulas, Yang-Taylor series and local fractional Laurent's series of complex functions in complex fractal space, and generalized residue theorems are investigated.