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Fractal Fract
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New Challenges Arising in Engineering Problems with Fractional and Integer...
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New Challenges Arising in Engineering Problems with Fractional and Integer Order, 4th Edition

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

Deadline for manuscript submissions: 30 September 2025 | Viewed by 2372

Special Issue Editors

Prof. Dr. Haci Mehmet Baskonus

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Guest Editor
Department of Mathematics, Faculty of Education, Harran University, Sanliurfa 63100, Turkey
Interests: partial differential equations; fractional calculus; analytical methods; numerical methods; mathematical physics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Luis Manuel Sánchez Ruiz

E-Mail Website1 Website2
Guest Editor
ETSID-Department of Applied Mathematics, Universitat Politecnica de Valencia, 46022 Valencia, Spain
Interests: fractional calculus; analytical and computational methods; differential and difference equations; real and complex analysis; applied and computational mathematics; mathematical physics
Special Issues, Collections and Topics in MDPI journals
Dr. Armando Ciancio

E-Mail Website
Guest Editor
Department of Biomedical and Dental Sciences and Morphofunctional Imaging, University of Messina, 98125 Messina, Italy
Interests: time series based on wavelets; analysis of solutions in the field of physical-mathematical models of rheological media; fractional calculus; mathematical models in economics and finance; physical-mathematical models for biological media and applications to biotechnological and medical sciences
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Recently, many new models have been developed to address real-world problems that represent serious threats to the future of humankind. These result from modeling events observed in various fields of science, such as physics, chemistry, mechanics, electricity, biology, economy, mathematical applications, and control theory. Moreover, research conducted on fractional ordinary or partial differential equations and other relevant topics relating to integer order has attracted the attention of experts from all over the world.

The focus of this Special Issue will be on reviewing new developments based on fractional differentiation and integration with respect to both theoretical and numerical aspects.

This Special Issue invites experts to share new ideas on theories, applications, numerical and analytical methods, and simulations of fractional calculus and fractional differential equations, as well as integer order. Topics of interest are defined below, and submissions relating to relevant fields are welcome.

  • New analytical and numerical methods to solve partial differential equations.
  • Computational methods for fractional differential equations.
  • The analysis, modeling, and control of phenomena in the following areas:
    • Electrical engineering;
    • Fluid dynamics and thermal engineering;
    • Mechanics;
    • Biology;
    • Physics;
    • Applied sciences;
    • Computer science.
  • Engineering problems.
  • Deterministic and stochastic fractional order models.

Prof. Dr. Haci Mehmet Baskonus
Prof. Dr. Luis Manuel Sánchez Ruiz
Dr. Armando Ciancio
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

  • new analytical and numerical methods to solve partial differential equations
  • computational methods for fractional differential equations
  • the analysis, modeling, and control of phenomena in the following areas
  • engineering problems
  • deterministic and stochastic fractional order models

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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

23 pages, 2348 KiB  
Article
Chaotic Analysis and Wave Photon Dynamics of Fractional Whitham–Broer–Kaup Model with β Derivative
by Muhammad Idrees Afridi, Theodoros E. Karakasidis and Abdullah Alhushaybari
Fractal Fract. 2025, 9(5), 287; https://doi.org/10.3390/fractalfract9050287 - 27 Apr 2025
Viewed by 163
Abstract
This study uses a conformable derivative of order β to investigate a fractional Whitham–Broer–Kaup (FWBK) model. This model has significant uses in several scientific domains, such as plasma physics and nonlinear optics. The enhanced modified Sardar sub-equation EMSSE approach is applied [...] Read more.
This study uses a conformable derivative of order β to investigate a fractional Whitham–Broer–Kaup (FWBK) model. This model has significant uses in several scientific domains, such as plasma physics and nonlinear optics. The enhanced modified Sardar sub-equation EMSSE approach is applied to achieve precise analytical solutions, demonstrating its effectiveness in resolving complex wave photons. Bright, solitary, trigonometric, dark, and plane waves are among the various wave dynamics that may be effectively and precisely determined using the FWBK model. Furthermore, the study explores the chaotic behaviour of both perturbed and unperturbed systems, revealing illumination on their dynamic characteristics. By demonstrating its validity in examining wave propagation in nonlinear fractional systems, the effectiveness and reliability of the suggested method in fractional modelling are confirmed through thorough investigation. Full article
(This article belongs to the Special Issue New Challenges Arising in Engineering Problems with Fractional and Integer Order, 4th Edition)
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18 pages, 3859 KiB  
Article
The Use of Artificial Intelligence in Data Analysis with Error Recognitions in Liver Transplantation in HIV-AIDS Patients Using Modified ABC Fractional Order Operators
by Hasib Khan, Jehad Alzabut, D. K. Almutairi and Wafa Khalaf Alqurashi
Fractal Fract. 2025, 9(1), 16; https://doi.org/10.3390/fractalfract9010016 - 30 Dec 2024
Cited by 12 | Viewed by 774
Abstract
In this article, we focused on the fractional order modeling, simulations and neural networking to observe the correlation between severity of infection in HIV-AIDS patients and the role of treatments and control. The model is structured with eight classes and a modified Atangana–Baleanu [...] Read more.
In this article, we focused on the fractional order modeling, simulations and neural networking to observe the correlation between severity of infection in HIV-AIDS patients and the role of treatments and control. The model is structured with eight classes and a modified Atangana–Baleanu derivative in Caputo’s sense. The model has several interlinking parameters which show the rates of transmission between classes. We assumed natural death and death on the disease severity in patients. The model was analyzed mathematically as well as computationally. In the mathematical aspects, R0 was plotted for different cases which play a vital role in the infection spread in the population. The model was passed through qualitative analysis for the existence of solutions and stability results. A computational scheme is developed for the model and is applied for the numerical results to analyze the intricate dynamics of the infection. It has been observed that there is a good resemblance in the results for the correlation between the hospitalization, vaccination and recovery rate of the patients. These are reaffirmed with the neural networking tools for the regression, probability, clustering, mean square error and fitting data. Full article
(This article belongs to the Special Issue New Challenges Arising in Engineering Problems with Fractional and Integer Order, 4th Edition)
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19 pages, 404 KiB  
Article
Modeling of (n,m)-Type Minkowski Pythagorean Hodograph Curves with Hopf Map and Applications
by Muhammed Talat Sariaydin and Aziz Yazla
Fractal Fract. 2024, 8(12), 705; https://doi.org/10.3390/fractalfract8120705 - 28 Nov 2024
Viewed by 822
Abstract
In the present paper, regular spacelike spatial Minkowski Pythagorean hodograph (MPH) curves are characterized with rational rotation-minimizing frames (RRMFs). We define an Euler–Rodrigues frame (ERF) for MPH curves and by means of this concept, we reach the definition of MPH curves of type [...] Read more.
In the present paper, regular spacelike spatial Minkowski Pythagorean hodograph (MPH) curves are characterized with rational rotation-minimizing frames (RRMFs). We define an Euler–Rodrigues frame (ERF) for MPH curves and by means of this concept, we reach the definition of MPH curves of type (n,m). Expressing the conditions provided by these curves in the form of a Minkowski–Hopf map that we define; it is aimed to establish a connection with the Lorentz force that occurs during the process of computer numerical control (CNC)-type sinker electronic discharge machines (EDMs). This approach is reinforced by split quaternion polynomials. We give conditions satisfied by MPH curves of low degree to be type (n,m) and construct illustrative examples. In five-axis CNC machines, rotation-minimizing frames are used for tool path planning, and in this way, unnecessary rotations in the tool frame are prevented and tool orientation is provided. Since we obtain MPH curves with RRMF using the ERF, finally we define the Fermi–Walker derivative and parallelism along MPH curves with respect to the ERF and give applications. Full article
(This article belongs to the Special Issue New Challenges Arising in Engineering Problems with Fractional and Integer Order, 4th Edition)
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