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
Feature Papers for Mathematical Physics Section 2026
share announcement

Feature Papers for Mathematical Physics Section 2026

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

Deadline for manuscript submissions: 31 October 2026 | Viewed by 1822

Special Issue Editor

Prof. Dr. Haci Mehmet Baskonus

grade E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Education, Harran University, 63100 Sanliurfa, Turkey
Interests: partial differential equations; fractional calculus; analytical methods; numerical methods; mathematical physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Science is a unique way to understand nature. In order to solve issues in the real world, engineers and experts conduct research to create new tools and determine the characteristics of scientific norms. Such scientific action is required by humanity to address everyday issues. The first phase of this process is to comprehend norms of mathematical physics which makes it feasible to experience the power of science firsthand.

This Special Issue, titled “Feature Papers for Mathematical Physics Section 2026”, aims to publish high-quality papers covering aspects of mathematical physics containing integer or fractional order operators. We welcome submissions from Editorial Board Members and outstanding scholars invited by the Editorial Board and by the Editorial Office.

Prof. Dr. Haci Mehmet Baskonus
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

  • engineering problems
  • analytical methods
  • numerical methods
  • computational mathematics
  • nonlinear system and applied in physics
  • information science
  • communications theory
  • bioinformatics
  • health problems
  • networks
  • physics
  • engineering and applied sciences
  • economy
  • statistics
  • fractals
  • fractional calculus
  • nonlinear dynamical systems
  • graph theory
  • statistical learning theory
  • computation topics on energy and environmental science
  • artificial intelligence
  • data science
  • discrete dynamical system

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 (4 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

37 pages, 9047 KB  
Article
Analysis of a Fractional-Order Leslie–Gower Prey–Predator–Parasite System with Dual Delays and Reaction–Diffusion Dynamics: A Statistical Approach
by Salem Mubarak Alzahrani, Ghaliah Alhamzi, Mona Bin-Asfour, Mansoor Alsulami, Khdija O. Taha, Najat Almutairi and Sayed Saber
Fractal Fract. 2026, 10(5), 303; https://doi.org/10.3390/fractalfract10050303 - 29 Apr 2026
Abstract
Thisarticle develops and analyzes a fractional-order Leslie–Gower prey–predator–parasite system incorporating two discrete delays and nonlocal spatial diffusion. The model’s central novelty lies in the simultaneous integration of three biologically realistic features that have not previously been combined: (i) fractional-order memory effects via a [...] Read more.
Thisarticle develops and analyzes a fractional-order Leslie–Gower prey–predator–parasite system incorporating two discrete delays and nonlocal spatial diffusion. The model’s central novelty lies in the simultaneous integration of three biologically realistic features that have not previously been combined: (i) fractional-order memory effects via a Caputo derivative of order α∈(0,1], (ii) two distinct biological delays—an infection transmission delay τ1 and a predator handling delay τ2—and (iii) nonlocal spatial dispersal modeled through fractional Laplacian operators (−Δ)γ/2. This triple integration enables the model to capture long-range temporal memory, delayed biological responses, and nonlocal spatial interactions simultaneously, offering insights into dynamics that are challenging to capture with classical integer-order or single-delay formulations. The fractional Laplacian generalizes classical diffusion by allowing long-range dispersal events (Lévy flights), where individuals can occasionally move over large distances with heavy-tailed step-size distributions—a phenomenon observed in many animal movement patterns but absent from standard diffusion models. We provide rigorous proofs of solution existence, uniqueness, non-negativity, and boundedness in both temporal and spatiotemporal settings. Local asymptotic stability conditions are derived for all feasible equilibrium states via characteristic equation analysis. The coexistence equilibrium undergoes a Hopf bifurcation when either delay crosses a critical threshold, with fractional order α modulating the bifurcation point and post-bifurcation oscillation frequency. A Lyapunov functional demonstrates global asymptotic stability of the infection-free equilibrium under biologically interpretable conditions. Turing instability analysis reveals conditions for spontaneous pattern formation, with the fractional exponent γ controlling pattern wavelength and correlation length. Numerical simulations validate theoretical predictions, including spatial patterns, traveling waves, and chaos. To bridge theory with potential applications, we outline a statistical framework for parameter estimation and uncertainty quantification, suggesting that β, α, and τ1 may be priority targets for parameter estimation. Full article
(This article belongs to the Special Issue Feature Papers for Mathematical Physics Section 2026)
►▼ Show Figures

Figure 1

28 pages, 702 KB  
Article
A Hybrid Neural Network Approach to Controllability in Caputo Fractional Neutral Integro-Differential Systems for Cryptocurrency Forecasting
by Prabakaran Raghavendran and Yamini Parthiban
Fractal Fract. 2026, 10(4), 268; https://doi.org/10.3390/fractalfract10040268 - 18 Apr 2026
Viewed by 298
Abstract
This research paper demonstrates how to manage Caputo fractional neutral integro-differential equations which include both integral and nonlinear elements through a unified framework that models dynamic systems with memory-based dynamics. The research establishes sufficient conditions for controllability through fixed point theory in a [...] Read more.
This research paper demonstrates how to manage Caputo fractional neutral integro-differential equations which include both integral and nonlinear elements through a unified framework that models dynamic systems with memory-based dynamics. The research establishes sufficient conditions for controllability through fixed point theory in a Banach space framework which requires particular assumptions while the study focuses on the K1<1 condition which leads to the existence of a controllable solution. The proposed criteria are demonstrated through a numerical example which tests the theoretical results. The real-world case study uses artificial neural network (ANN) technology to predict Litecoin prices through the application of the fractional controllability model which analyzes historical financial data. The hybrid framework enables precise forecasting of nonlinear time series because it combines fractional calculus mathematical principles with ANN learning abilities. The proposed method demonstrates its predictive efficiency. The method shows robust performance through experimental results using cross-validation and performance metrics. The proposed model demonstrates competitive performance while providing additional advantages such as incorporation of memory effects and theoretical controllability. The research establishes a novel connection between fractional dynamical systems and machine learning which serves as an essential tool for studying complicated systems in theoretical research and practical applications. Full article
(This article belongs to the Special Issue Feature Papers for Mathematical Physics Section 2026)
►▼ Show Figures

Figure 1

16 pages, 1399 KB  
Article
Chaotic and Fractal Evidence from Turkiye’s Macroeconomic System: Chaos-Augmented Phillips Curve
by Melike Elif Bildirici, Merve Çolak and Elçin Aykaç Alp
Fractal Fract. 2026, 10(3), 138; https://doi.org/10.3390/fractalfract10030138 - 25 Feb 2026
Viewed by 491
Abstract
The paper explored the fractal, nonlinear and chaotic dynamics between oil prices, inflation, economic growth and unemployment in Turkiye from 1960 to 2024 and examined how energy market volatility propagated through the macroeconomy via complex, regime-dependent mechanisms. It developed a chaotic regression method [...] Read more.
The paper explored the fractal, nonlinear and chaotic dynamics between oil prices, inflation, economic growth and unemployment in Turkiye from 1960 to 2024 and examined how energy market volatility propagated through the macroeconomy via complex, regime-dependent mechanisms. It developed a chaotic regression method and employed entropy-based measures (Shannon, Rényi and Tsallis), Lyapunov exponents, Lorenz and Rössler attractors, Julia set diagnostics and the chaos Granger causality test (Hiemstra–Jones). By nesting entropy, chaos and causality within a unified framework, it contributed methodological innovations and practical insights to the energy–economy literature. The chaotic regression results revealed that oil price shocks generated asymmetric and nonlinear responses in inflation, unemployment and growth that were characterized by chaos and sensitivity to initial conditions and demonstrated that oil shocks act as catalysts for nonlinear propagation and fractal macroeconomic dynamics. Julia set results determined that unemployment can be explained by inflation fractal size. Hiemstra–Jones method determined unidirectional causality from oil to both inflation, economic growth and unemployment. According to the results, adopting nonlinear and chaos-based modeling approaches is essential to understand the macroeconomic consequences of energy shocks. For policymakers, the evidence determined that the costs of disinflation or inflation control are sensitive to energy market volatility. The paper contributed to the energy–economy-econometrics literature by integrating entropy, chaos and causality analyses into the oil price–macroeconomy nexus by offering both methodological innovations and practical insights. Full article
(This article belongs to the Special Issue Feature Papers for Mathematical Physics Section 2026)
►▼ Show Figures

Figure 1

17 pages, 13236 KB  
Article
Influence of Initial Stress on Wave Propagation in Microelongated Thermo-Elastic Media Under the Refined Fractional Dual Phase Lag Model
by Mohamed F. Ismail, Hamdy M. Ahmed, Taha Radwan, Soliman Alkhatib, M. Elsaid Ramadan and Eslam Nabil Shawki El-Ganzoury
Fractal Fract. 2026, 10(1), 30; https://doi.org/10.3390/fractalfract10010030 - 4 Jan 2026
Cited by 2 | Viewed by 473
Abstract
This paper focuses on analyzing how initial stress influences wave propagation phenomena in a microelongated thermoelastic medium described within the framework of fractional conformable derivative, considering both the dual phase lag (DPL) and refined dual phase lag (RDPL) theories. The fundamental governing equations [...] Read more.
This paper focuses on analyzing how initial stress influences wave propagation phenomena in a microelongated thermoelastic medium described within the framework of fractional conformable derivative, considering both the dual phase lag (DPL) and refined dual phase lag (RDPL) theories. The fundamental governing equations for heat transfer, mechanical motion, and microelongation are established to incorporate finite thermal wave speed and microelongation effects. Through an appropriate non-dimensionalization procedure and the application of the normal mode analysis technique, the coupled partial differential system is transformed into a form that admits explicit analytical solutions. These solutions provide expressions for displacement, microelongation, temperature distribution, and stress components, allowing a comprehensive examination of the thermomechanical wave behavior within the medium. To better comprehend the theoretical results, numerical evaluations are performed to emphasize the comparison of DPL and RDPL in the presence and absence of initial stress, as well as the influence of the fractional-order parameter and different times on wave properties. The results show that initial stress has a considerable effect on wave propagation characteristics such as amplitude modulation, propagation speed, and attenuation rate. Furthermore, the use of fractional conformable derivatives and the RDPL formulation allows for more precise modeling and control of the thermal relaxation dynamics. The current study contributes to a better understanding of the linked microelongated and thermal effects in thermoelastic media, as well as significant insights for designing and modeling advanced microscale thermoelastic systems. Full article
(This article belongs to the Special Issue Feature Papers for Mathematical Physics Section 2026)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-4
Back to TopTop