Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.6
3.6
Journals
Fractal Fract
Special Issues
Fractal Functions: Theoretical Research and Application Analysis
share announcement

Fractal Functions: Theoretical Research and Application Analysis

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".

Deadline for manuscript submissions: 31 October 2025 | Viewed by 1542

Special Issue Editors

Prof. Dr. Yong-Shun Liang

E-Mail Website
Guest Editor
School of Mathematics and Statistics; Nanjing University of Science and Technology, Nanjing 210094, China
Interests: fractional calculus on fractal functions; fractal geometry; fractal dimensions; function approximation theory
Prof. Dr. Jia Liu

E-Mail Website
Guest Editor
Institute of statistics and applied mathematics, Anhui University of Finance and Economics, Bengbu 233030, China
Interests: fractal geometry; fractal functions; number theory

Special Issue Information

Dear Colleagues,

Fractal geometry is an important branch of mathematics that allows for the description of sets that are too intricate to fit into classical geometry. The concept of fractals was first introduced by Mandelbrot in the 1970s as a class of highly irregular sets, usually presenting with self-similarity, infinite complexity, and a non-integral fractal dimension. Up to now, it has been hugely significant for the development of a variety of sciences. In mathematics, fractals originate from chaos and dynamic systems. Soon after their discovery, they began to appear in almost every field and were systematically studied using classical and modern methods. In recent years, scholars have mainly focused on the following research objects: fractal dimensions of graphs, fractal interpolation and approximation, fractals and dynamical systems, self-similarity and Lipschitz equivalence, geometric measure theory, fractional calculus of fractal functions, fractal geometry, number theory, etc.

Fractal curves and fractal functions are a class of important research objects in fractal geometry. As is well known, fractal curves are widely distributed in nature, being found in lightning, snowflakes, coastlines, geological crack lines, and so on. In mathematical analysis, fractal functions are usually regarded as continuous functions of one variable based on a two-dimensional Cartesian coordinate system to probe their fractal characteristics. The fractal dimension, as a common measure of the geometric complexity of sets, can be an essential tool to describe their fractal characteristics. In recent years, fractal functions have been widely applied in other academic fields, such as physics, statistics, geology, material science, quantization theory, signal processing, computer image processing, pattern recognition, and more. Therefore, fractal functions have increasingly shown their tremendous research value for both real life and scientific development.

This Special Issue aims to collect a series of high-quality papers from renowned experts around the world to present the latest research on fractal functions with their application and analysis in various fields.

Prof. Dr. Yong-Shun Liang
Prof. Dr. Jia Liu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • iterated function systems
  • fractal interpolation functions
  • fractal functions
  • fractal surfaces
  • fractional calculus
  • function spaces
  • self-similar sets and measures
  • self-affine and self-conformal sets/measures
  • fractal approximation and modeling
  • quantization dimension
  • box dimension, Hausdorff dimension, and L^q dimensions
  • applications of the fractal functions to any areas of finance, engineering, economy, biology, etc.

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

15 pages, 560 KiB  
Article
Entropiesand Degree-Based Topological Indices of Generalized Sierpiński Graphs
by Si-Ao Xu, Jia-Dong Si and Jia-Bao Liu
Fractal Fract. 2025, 9(3), 190; https://doi.org/10.3390/fractalfract9030190 - 19 Mar 2025
Viewed by 308
Abstract
Fractals are geometric patterns that appear self-similar across all length scales and are constructed by repeating a single unit on a regular basis. Entropy, as a core thermodynamic function, is an extension based on information theory (such as Shannon entropy) that is used [...] Read more.
Fractals are geometric patterns that appear self-similar across all length scales and are constructed by repeating a single unit on a regular basis. Entropy, as a core thermodynamic function, is an extension based on information theory (such as Shannon entropy) that is used to describe the topological structural complexity or degree of disorder in networks. Topological indices, as graph invariants, provide quantitative descriptors for characterizing global structural properties. In this paper, we investigate two types of generalized Sierpiński graphs constructed on the basis of different seed graphs, and employ six topological indices—the first Zagreb index, the second Zagreb index, the forgotten index, the augmented Zagreb index, the Sombor index, and the elliptic Sombor index—to analyze the corresponding entropy. We utilize the method of edge partition based on vertex degrees and derive analytical formulations for the first Zagreb entropy, the second Zagreb entropy, the forgotten entropy, the augmented Zagreb entropy, the Sombor entropy, and the elliptic Sombor entropy. This research approach, which integrates entropy with Sierpiński network characteristics, furnishes novel perspectives and instrumental tools for addressing challenges in chemical graph theory, computer networks, and other related fields. Full article
(This article belongs to the Special Issue Fractal Functions: Theoretical Research and Application Analysis)
►▼ Show Figures

Figure 1

13 pages, 262 KiB  
Article
Progress on Fractal Dimensions of the Weierstrass Function and Weierstrass-Type Functions
by Yue Qiu and Yongshun Liang
Fractal Fract. 2025, 9(3), 143; https://doi.org/10.3390/fractalfract9030143 - 25 Feb 2025
Viewed by 539
Abstract
The Weierstrass function W(x)=∑n=1∞ancos(2πbnx) is a function that is continuous everywhere and differentiable nowhere. There are many investigations on fractal dimensions of the Weierstrass [...] Read more.
The Weierstrass function W(x)=∑n=1∞ancos(2πbnx) is a function that is continuous everywhere and differentiable nowhere. There are many investigations on fractal dimensions of the Weierstrass function, and the investigation of its Hausdorff dimension is still ongoing. In this paper, we summarize past researchers’ investigations on fractal dimensions of the Weierstrass function graph. Full article
(This article belongs to the Special Issue Fractal Functions: Theoretical Research and Application Analysis)
20 pages, 1031 KiB  
Article
Entropies and Degree-Based Topological Indices of Coronene Fractal Structures
by Si-Ao Xu and Jia-Bao Liu
Fractal Fract. 2025, 9(3), 133; https://doi.org/10.3390/fractalfract9030133 - 20 Feb 2025
Viewed by 370
Abstract
Molecular fractals are geometric patterns that appear self-similar across all length scales and are constructed by repeating a single unit on a regular basis. Entropy, as a core thermodynamic function, is an extension based on information theory (such as Shannon entropy) and is [...] Read more.
Molecular fractals are geometric patterns that appear self-similar across all length scales and are constructed by repeating a single unit on a regular basis. Entropy, as a core thermodynamic function, is an extension based on information theory (such as Shannon entropy) and is used to describe the topological structural complexity or degree of disorder in networks. A topological index is a numeric quantity associated with a network or a graph that characterizes its whole structural properties. In this study, we focus on fractal structures formed by systematically repeating a fixed unit of coronene, a polycyclic aromatic hydrocarbon composed of six benzene rings fused in a hexagonal pattern. In this paper, three types of coronal fractal structures, namely zigzag (ZHCF), armchair (AHCF), and rectangular (RCF), are studied, and their five degree-based topological indices and corresponding entropies are calculated. Full article
(This article belongs to the Special Issue Fractal Functions: Theoretical Research and Application Analysis)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-3
Back to TopTop