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Fractal Fract
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From Fractals to Fractional Calculus: Nonlinear Dynamics and Hybrid Complex...
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From Fractals to Fractional Calculus: Nonlinear Dynamics and Hybrid Complex Systems

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 December 2025 | Viewed by 1861

Special Issue Editor

Prof. Dr. Katica (Stevanović) Hedrih

E-Mail Website
Guest Editor
1. Department of Mechanics, Mathematical Institute of Serbian Academy of Science and Arts, 11000 Belgrade, Serbia
2. Faculty of Mechanical Engineering, University of Niš, 18000 Nis, Serbia
Interests: nonlinear science; mechanics; elastodynamics; electromechanical systems; fractional calculus

Special Issue Information

Dear Colleagues,

Beautiful images of fractals began to gain notoriety in the scientific literature three and a half decades ago with the widespread development of approximate numerical methods and software tools for solving systems of nonlinear differential equations. Today, the application of numerical methods reveals many nonlinear and rare phenomena and singularities in the dynamics of nonlinear dynamic systems. By reaffirming the differentiation of the fractional order in its application to the dynamics of continuums and discrete dynamic systems, we discover the benefits of elements of mathematical phenomenology and analogies in the dynamics of hybrid systems of complex structures in natural–mathematical, technical–technological, as well as biomedical sciences.

The goal of this Special Issue is to publish papers whose contents show similarities and analogies in the elements of mathematical phenomenology in various fields of science.

Topics that are invited for submission include (but are not limited to) the following:

  • Elements of the mathematical phenomenology and mapping of dynamics models in natural, mathematical, and technical sciences (model analogies);
  • Mathematical foundations of fractals and the fractional analysis of approximate solutions of nonlinear dynamics;
  • Fractals and applications;
  • Complex models of fractional-type materials;
  • Phenomena and modes in the dynamics of discrete and continuous dynamic systems as well as in nonlinear and fractional-type ones;
  • Modes of dynamics of fractional-type systems, both independent and with interactions;
  • Energy transfer between modes;
  • Dynamics of hybrid systems of complex structures;
  • Biological oscillators—linear, nonlinear, and fractional-type piezoelectric models.

Prof. Dr. Katica (Stevanović) Hedrih
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
  • nonlinear dynamics
  • fractional calculus
  • mathematical phenomenology
  • hybrid systems
  • complex structures
  • discrete and continuous dynamic systems

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

Published Papers (3 papers)

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Research

38 pages, 601 KB  
Article
A New Laplace-Type Transform on Weighted Spaces with Applications to Hybrid Fractional Cauchy Problems
by Samten Choden, Jakgrit Sompong, Ekkarath Thailert and Sotiris K. Ntouyas
Fractal Fract. 2025, 9(11), 751; https://doi.org/10.3390/fractalfract9110751 - 20 Nov 2025
Viewed by 474
Abstract
This paper develops a generalized Laplace transform theory within weighted function spaces tailored for the analysis of fractional differential equations involving the ψ-Hilfer derivative. We redefine the transform in a weighted setting, establish its fundamental properties—including linearity, convolution theorems, and action on [...] Read more.
This paper develops a generalized Laplace transform theory within weighted function spaces tailored for the analysis of fractional differential equations involving the ψ-Hilfer derivative. We redefine the transform in a weighted setting, establish its fundamental properties—including linearity, convolution theorems, and action on δψ derivatives—and derive explicit formulas for the transforms of ψ-Riemann–Liouville, ψ-Caputo, and ψ-Hilfer fractional operators. The results provide a rigorous analytical foundation for solving hybrid fractional Cauchy problems that combine classical and fractional derivatives. As an application, we solve a hybrid model incorporating both δψ derivatives and ψ-Hilfer fractional derivatives, obtaining explicit solutions in terms of multivariate Mittag-Leffler functions. The effectiveness of the method is illustrated through a capacitor charging model and a hydraulic door closer system based on a mass-damper model, demonstrating how fractional-order terms capture memory effects and non-ideal behaviors not described by classical integer-order models. Full article
(This article belongs to the Special Issue From Fractals to Fractional Calculus: Nonlinear Dynamics and Hybrid Complex Systems)
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15 pages, 1573 KB  
Article
Fractional Dynamics of Information Entropy in Quantum Wire System Under Rashba Interaction
by Rabie I. Mohamed, Ramy M. Hafez, Atef F. Hashem and Mahmoud Abdel-Aty
Fractal Fract. 2025, 9(11), 741; https://doi.org/10.3390/fractalfract9110741 - 17 Nov 2025
Viewed by 375
Abstract
We present a theoretical examination of the fractional dynamics of information entropy within a semiconductor nanowire system influenced by Rashba spin–orbit interaction and external magnetic fields. Moreover, we determine the fractional nanowire state through the analytical solution of the fractional Schrödinger equation, considering [...] Read more.
We present a theoretical examination of the fractional dynamics of information entropy within a semiconductor nanowire system influenced by Rashba spin–orbit interaction and external magnetic fields. Moreover, we determine the fractional nanowire state through the analytical solution of the fractional Schrödinger equation, considering various initial states of the nanowire system. Our research emphasizes the impact of the fractional order and the interaction parameters on the behavior of information entropy. Our findings reveal that the temporal behavior of information entropy is highly sensitive to any variations in the magnetic field length, the Rashba spin–orbit interaction, and the fractional order parameter. The results demonstrate that these parameters are pivotal in determining the coherence and correlation properties of the nanowire system. Therefore, precise control of these factors paves the way for enhancing entanglement performance and facilitating information transfer in spintronic and quantum communication applications. Full article
(This article belongs to the Special Issue From Fractals to Fractional Calculus: Nonlinear Dynamics and Hybrid Complex Systems)
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52 pages, 10216 KB  
Article
Rheologic Fractional Oscillators or Creepers
by Katica R. (Stevanović) Hedrih
Fractal Fract. 2025, 9(8), 552; https://doi.org/10.3390/fractalfract9080552 - 21 Aug 2025
Cited by 1 | Viewed by 636
Abstract
Using the newly introduced, by the author, basic complex and hybrid complex rheologic models of the fractional type, the dynamics of a series of mechanical rheologic discrete dynamical systems of the fractional type (RDDSFT) of rheologic oscillators (ROFTs) or creepers (RCFTs), with corresponding [...] Read more.
Using the newly introduced, by the author, basic complex and hybrid complex rheologic models of the fractional type, the dynamics of a series of mechanical rheologic discrete dynamical systems of the fractional type (RDDSFT) of rheologic oscillators (ROFTs) or creepers (RCFTs), with corresponding independent generalized coordinates (IGCs) and external (IGCEDF) and internal (IGCIGF) degrees of freedom of movement, were studied. Laplace transformations of solutions for independent generalized coordinates (IGCs), as well as external (IGCEDFs) and internal (IGCIDF) degrees of freedom of system dynamics, were determined. On the studied specimens, it was shown that rheologic complex models of the fractional type introduce internal degrees of freedom into the dynamics of rheologic discrete dynamical systems. New challenges appear for mathematicians, such as translating the Laplace transformations of solutions for independent generalized coordinates (LTIGCs) into the time domain. A number of translations of Laplace transformations of solutions into the time domain were performed by the author of this paper. A series of characteristic surfaces of elongations of Laplace transformations of independent generalized coordinates (IGCs) of the dynamics of rheologic discrete dynamic systems of the rheologic oscillator type, i.e., the rheologic creeper type, is shown as a function of fractional order differentiation exponent and Laplace transformation parameter. This manuscript presents the scientific results of theoretical research on the dynamics of rheologic discrete dynamic systems of the fractional type that was conducted using new models and a rigorous mathematical analytical analysis with fractional-order differential equations (DEFOs) and Laplace transformations (LTs). These results can contribute to new experimental research and materials technologies. A separate section presents the theoretical foundations of the methods and methodologies used in this research, without the details that can be found in the author’s previously published works. Full article
(This article belongs to the Special Issue From Fractals to Fractional Calculus: Nonlinear Dynamics and Hybrid Complex Systems)
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