Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
6.0
3.3
Journals
Fractal Fract
Special Issues
Time-Fractal and Fractional Models in Physics and Engineering
share announcement

Time-Fractal and Fractional Models in Physics and Engineering

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

Deadline for manuscript submissions: 31 December 2025 | Viewed by 2859

Special Issue Editor

Prof. Dr. Kyungsik Kim

E-Mail Website
Guest Editor
Department of Physics, Pukyong National University, Busan 48513, Republic of Korea
Interests: multifractal analysis; stochastic processes; nonlinear dynamics; econophysics; complex network

Special Issue Information

Dear Colleagues,

This Special Issue titled "Time-Fractal and Fractional Models in Physics and Engineering" covers concepts and models in the fields of fractals, multifractals, DFA, MCCA, and fractional analysis in natural science, engineering, social science, and econophysics. It includes complex networks related to fractals in transportation and civil engineering and introduces the theoretical and computer-simulated method of fractals, which is currently an active field of research. Among the applied fields, neural network applications pertain to object and image recognition in social sciences and the economic physics fields of stocks, exchange rates, futures, and bitcoin.

The focus of this Special Issue is to continue to advance research on topics related to theory, design, implementation, and application in the above fields. The topics that submissions may cover include (but are not limited to) the following：

  • Fractals, multifractals, DFA, MCCA, fractional analysis;
  • Fractals of anomalous transport in stochastic process, thermodynamics and statistical mechanics;
  • Fractals in social, civil, engineering and space systems;
  • Fractals and multifractals in complex networks;
  • Fractals in machine learning and artificial intelligence;
  • Fractals in fluid dynamics, energy, climate and global change;
  • Multifractals regarding stock, the exchange rate, futures, cryptocurrency, etc., in econophysics;
  • Fractals in medical sciences and brain networks;
  • Fractal dynamics of time series data in chaos theory.

Research papers and review papers should be approximately 15 pages long. Short notes and letters should be approximately 7 pages long.

Prof. Dr. Kyungsik Kim
Guest Editor

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 250 words) can be sent to the Editorial Office for assessment.

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

  • fractals, multifractals, MDFA, MDCCA, fractional analysis
  • thermodynamics, statistical mechanics
  • machine learning, artificial intelligence
  • complex network
  • image recognition
  • fluid climate and global change
  • econophysics
  • brain network

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.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

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

Published Papers (5 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

40 pages, 560 KB  
Article
On the Motion of a Charged Colloid with a Harmonic Trap
by Yun Jeong Kang, Sung Kyu Seo, Sungchul Kwon and Kyungsik Kim
Fractal Fract. 2025, 9(12), 788; https://doi.org/10.3390/fractalfract9120788 - 1 Dec 2025
Viewed by 189
Abstract
In this study, we derive the Fokker–Planck equation for a colloidal particle subject to a harmonic trap and viscous forces under the influence of a magnetic field. We then extend the analysis to a charged colloid driven by both thermal and active noises [...] Read more.
In this study, we derive the Fokker–Planck equation for a colloidal particle subject to a harmonic trap and viscous forces under the influence of a magnetic field. We then extend the analysis to a charged colloid driven by both thermal and active noises in the same magnetic environment. Finally, the case of a charged colloid experiencing a harmonic trap together with thermal and active noises is investigated. Analytical solutions for the joint probability density are obtained in the limits of t≪τ, t≫τ, and τ=0. For a colloid under a harmonic trap and magnetic field, the mean squared displacement exhibits a superdiffusive scaling proportional to t3 in the short-time regime (t≪τ), while the mean squared velocity scales as ∼t when τ=0. For a charged colloid with thermal noise, the mean-squared displacement follows a superdiffusive form ∼t2h+1 for t≪τ, and the mean squared velocity again scales linearly with time for τ=0. When the active noise is included together with a harmonic trap, the characteristic time scale grows as ∼t4 in the short-time regime, while the mean squared velocity becomes normally diffusive at τ=0. In the long-time limit (t≫τ) and for τ=0, the moments of the joint probability density under combined thermal and active noises scale as ∼t4h+2, consistent with our analytical results. Notably, as h→1/2, the entropy of the joint probability density with thermal noise ζth(t) coincides with that obtained for active noise ζac(t) in both t≫τ and τ=0 limits. Full article
(This article belongs to the Special Issue Time-Fractal and Fractional Models in Physics and Engineering)
21 pages, 20180 KB  
Article
Season-Resolved, Fluctuation-Level Regional Connectivity of PM2.5 over the Korean Peninsula Revealed by Multifractal Detrended Cross-Correlation Networks (2016–2020)
by Gyuchang Lim and Seungsik Min
Fractal Fract. 2025, 9(11), 737; https://doi.org/10.3390/fractalfract9110737 - 14 Nov 2025
Viewed by 414
Abstract
Motivated by the strong seasonality of East Asian meteorology and its control on pollution episodes characterized by fluctuation level, we model the season-resolved climatology of the regional PM2.5 connectivity over the Korean Peninsula. Using daily AirKorea data for 2016–2020, we (i) remove [...] Read more.
Motivated by the strong seasonality of East Asian meteorology and its control on pollution episodes characterized by fluctuation level, we model the season-resolved climatology of the regional PM2.5 connectivity over the Korean Peninsula. Using daily AirKorea data for 2016–2020, we (i) remove daily climatology and the peninsula-wide background (empirical orthogonal function; EOF1) to obtain residual signals; (ii) compute the sign-preserving multifractal detrended cross-correlation coefficient MFDCCA-ρq,s; (iii) apply iAAFT surrogate significance across scales; and (iv) construct signed, weighted networks aggregated over short (5–15 d) and mid (15–30 d) bands for DJF/MAM/JJA/SON. Our analysis targets the seasonal climatology of fluctuation-level (q-dependent) connectivity by pooling seasons across years; this approach increases statistical robustness at 5–30-day scales and avoids diluting season-specific organization. We find negligible connectivity for q<0 (small fluctuations) but dense, seasonally organized networks for q>0 (strongest in winter–spring and at 15–30 days). After removing the EOF1, positive subgraphs form assortative regional backbones, while negative subgraphs reveal a northwest–southeast anti-phase dipole; the connectivity around Baengnyeongdo (B) highlights a transboundary sentinel role in cool seasons. These results demonstrate that a season-resolved, fluctuation-level framework effectively isolates regional connectivity that would otherwise be masked in annual aggregates or by the peninsula-wide background. Full article
(This article belongs to the Special Issue Time-Fractal and Fractional Models in Physics and Engineering)
►▼ Show Figures

Figure 1

25 pages, 4526 KB  
Article
The Tantawy Technique for Modeling Fractional Kinetic Alfvén Solitary Waves in an Oxygen–Hydrogen Plasma in Earth’s Upper Ionosphere
by Shaukat Ali Shan, Wedad Albalawi, Rania A. Alharbey and Samir A. El-Tantawy
Fractal Fract. 2025, 9(11), 705; https://doi.org/10.3390/fractalfract9110705 - 31 Oct 2025
Viewed by 420
Abstract
Kinetic Alfvén waves (KAWs) are investigated in an Oxygen–Hydrogen plasma with electrons following the behavior of rq-distribution in an upper ionosphere. We aim to study low-frequency and long wavelengths at 1700 kms in the upper ionosphere of Earth as detected by [...] Read more.
Kinetic Alfvén waves (KAWs) are investigated in an Oxygen–Hydrogen plasma with electrons following the behavior of rq-distribution in an upper ionosphere. We aim to study low-frequency and long wavelengths at 1700 kms in the upper ionosphere of Earth as detected by Freja satellite. The fluid model and reductive perturbation method are combined to obtain the evolutionary wave equations that can be used to describe both fractional and non-fractional KAWs in an Oxygen–Hydrogen ion plasma. This procedure is used to obtain the integer-order Korteweg–de Vries (KdV) equation and then analyze its solitary wave solution. In addition, this study is carried out to evaluate the fractional KdV (FKdV) equation using a new approach called the “Tantawy technique” in order to generate more stable and highly accurate approximations that will be utilized to accurately depict physical events. This investigation also helps locate the existence regions of the solitary waves (SWs), and in turn displays that the characteristics of KAWs are affected by a number of physical factors, such as the nonthermal parameters/spectral indices “r”, “q”, and obliqueness (characterized by lz). Depending on the parameter governing the distribution, especially the nonthermality of inertialess electrons, the rq-distribution of electrons has a major impact on the properties of KAWs. Full article
(This article belongs to the Special Issue Time-Fractal and Fractional Models in Physics and Engineering)
►▼ Show Figures

Figure 1

23 pages, 6605 KB  
Article
Wintertime Cross-Correlational Structures Between Sea Surface Temperature Anomaly and Atmospheric-and-Oceanic Fields in the East/Japan Sea Under Arctic Oscillation
by Gyuchang Lim and Jong-Jin Park
Fractal Fract. 2025, 9(11), 684; https://doi.org/10.3390/fractalfract9110684 - 23 Oct 2025
Viewed by 500
Abstract
The winter Arctic Oscillation (AO) modulates the East Asian climate and the East/Japan Sea (EJS) thermodynamics, yet the local, scale-dependent air–sea couplings remain unclear. Using 30 years of daily fields (1993–2022), we map at each grid point, the cross-persistence and scale-dependent cross-correlations between [...] Read more.
The winter Arctic Oscillation (AO) modulates the East Asian climate and the East/Japan Sea (EJS) thermodynamics, yet the local, scale-dependent air–sea couplings remain unclear. Using 30 years of daily fields (1993–2022), we map at each grid point, the cross-persistence and scale-dependent cross-correlations between sea surface temperature anomalies (SSTA) and (i) atmospheric anomalies, (ii) turbulent heat-flux anomalies (sensible and latent), and (iii) oceanic anomalies. Detrended Fluctuation/Cross-Correlation Analyses (DFA/DCCA, 5–50 days) yield the Hurst exponent (H, hXY) and the DCCA coefficient (ρdcca). Significance is assessed with iterative-AAFT surrogates and Benjamini–Hochberg false discovery rate (FDR). Three robust features emerge: (1) during AO+, the East Korean Bay–Subpolar Front corridor shows large SSTA variance and high long-term memory (H≥ 1.5); (2) turbulent heat-flux anomalies are anti-phased with SSTA and show little cross-persistence; (3) among oceanic fields, SSHA and meridional geostrophic velocity provide the most AO-robust positive coupling. Within a fractal frame, DFA slopes (1<H<2) quantify local self-similarity; interpreting winter anomalies as fBm implies a fractal-dimension proxy D=3−H, so AO+ hot spots exhibit D≤1.5. These fractal maps, together with ρdcca, offer a compact way to pre-locate marine-heatwave-prone regions. The grid-point, FDR-controlled DFA/DCCA approach is transferable to other marginal seas. Full article
(This article belongs to the Special Issue Time-Fractal and Fractional Models in Physics and Engineering)
►▼ Show Figures

Figure 1

15 pages, 2416 KB  
Article
Boundary Element Method Solution of a Fractional Bioheat Equation for Memory-Driven Heat Transfer in Biological Tissues
by Mohamed Abdelsabour Fahmy and Ahmad Almutlg
Fractal Fract. 2025, 9(9), 565; https://doi.org/10.3390/fractalfract9090565 - 28 Aug 2025
Cited by 2 | Viewed by 900
Abstract
This work develops a Boundary Element Method (BEM) formulation for simulating bioheat transfer in perfused biological tissues using the Atangana–Baleanu fractional derivative in the Caputo sense (ABC). The ABC operator incorporates a nonsingular Mittag–Leffler kernel to model thermal memory effects while preserving compatibility [...] Read more.
This work develops a Boundary Element Method (BEM) formulation for simulating bioheat transfer in perfused biological tissues using the Atangana–Baleanu fractional derivative in the Caputo sense (ABC). The ABC operator incorporates a nonsingular Mittag–Leffler kernel to model thermal memory effects while preserving compatibility with standard boundary conditions. The formulation combines boundary discretization with cell-based domain integration to account for volumetric heat sources, and a recursive time-stepping scheme to efficiently evaluate the fractional term. The model is applied to a one-dimensional cylindrical tissue domain subjected to metabolic heating and external energy deposition. Simulations are performed for multiple fractional orders, and the results are compared with classical BEM (a=1.0), Caputo-based fractional BEM, and in vitro experimental temperature data. The fractional order a≈0.894 yields the best agreement with experimental measurements, reducing the maximum temperature error to 1.2% while maintaining moderate computational cost. These results indicate that the proposed BEM–ABC framework effectively captures nonlocal and time-delayed heat conduction effects in biological tissues and provides an efficient alternative to conventional fractional models for thermal analysis in biomedical applications. Full article
(This article belongs to the Special Issue Time-Fractal and Fractional Models in Physics and Engineering)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-5
Back to TopTop