A generalized model for Yang-Fourier transforms in fractal space

TL;DR

This paper introduces a generalized Yang-Fourier transform model based on local fractional calculus, enabling analysis of continuous but nowhere differentiable functions in fractal spaces, expanding mathematical tools for fractal analysis.

Contribution

The paper develops a new generalized model for Yang-Fourier transforms in fractal space derived from local fractional calculus, extending existing Fourier analysis methods.

Findings

Derived a generalized Yang-Fourier transform model.

Analyzed local fractional continuous non-differentiable functions.

Proposed detailed results for the generalized model.

Abstract

Local fractional calculus deals with everywhere continuous but nowhere differentiable functions in fractal space. The Yang-Fourier transform based on the local fractional calculus is a generalization of Fourier transform in fractal space. In this paper, local fractional continuous non-differentiable functions in fractal space are studied, and the generalized model for the Yang-Fourier transforms derived from the local fractional calculus are introduced. A generalized model for the Yang-Fourier transforms in fractal space and some results are proposed in detail.