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Fractal Fract
Special Issues
Recent Computational Methods for Fractal and Fractional Nonlinear Partial Differential...
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Recent Computational Methods for Fractal and Fractional Nonlinear Partial Differential Equations

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

Deadline for manuscript submissions: 31 July 2025 | Viewed by 1220

Special Issue Editors

Dr. Kang-Jia Wang

E-Mail Website
Guest Editor
School of Physics and Electronic Information Engineering; Henan Polytechnic University, Jiaozuo 454003, China
Interests: fractal and fractional calculus; nonlinear vibration
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Inés Tejado

E-Mail Website
Guest Editor
Industrial Engineering School, University of Extremadura, 06006 Badajoz, Spain
Interests: fractional dynamics; fractional-order nonlinear systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nonlinear partial differential equations (NPDEs) are an important branch of modern mathematics and are currently the main focus of differential equation research, including integer order partial differential equations and fractal and fractional NPDEs. Fractal and fractional NPDEs are derivatives and extensions of traditional nonlinear integer order differential equations, and their properties are more complex than traditional nonlinear integer order equations. In recent years, the exact solutions of the NPDEs have been a focus of research. This special issue, therefore, calls for the submission of high-quality research papers with an emphasis on the latest developments of the computational methods for fractal and fractional NPDEs. Topics include, but are not limited to, the following:

  1. Methods for the fractal and fractional nonlinear partial differential equations;
  2. Fractal and fractional partial differential equations in physics;
  3. Advanced theory of fractal and fractional calculus;
  4. Fractal variational principle;
  5. Fractal and fractional soliton solutions;
  6. Travelling wave solutions;
  7. Chaotic behaviors of the fractal and fractional partial differential equations;
  8. Two-scale transform.

Dr. Kang-Jia Wang
Prof. Dr. Inés Tejado
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

  • fractal and fractional nonlinear partial differential equations
  • fractal and fractional calculus
  • mathematical physics
  • fractal variational principle

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Published Papers (2 papers)

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Research

17 pages, 1168 KiB  
Article
Analytical Solitary Wave Solutions of Fractional Tzitzéica Equation Using Expansion Approach: Theoretical Insights and Applications
by Wael W. Mohammed, Mst. Munny Khatun, Mohamed S. Algolam, Rabeb Sidaoui and M. Ali Akbar
Fractal Fract. 2025, 9(7), 438; https://doi.org/10.3390/fractalfract9070438 - 3 Jul 2025
Cited by 1 | Viewed by 232
Abstract
In this study, we investigate the fractional Tzitzéica equation, a nonlinear evolution equation known for modeling complex phenomena in various scientific domains such as solid-state physics, crystal dislocation, electromagnetic waves, chemical kinetics, quantum field theory, and nonlinear optics. Using the (G′/ [...] Read more.
In this study, we investigate the fractional Tzitzéica equation, a nonlinear evolution equation known for modeling complex phenomena in various scientific domains such as solid-state physics, crystal dislocation, electromagnetic waves, chemical kinetics, quantum field theory, and nonlinear optics. Using the (G′/G, 1/G)-expansion approach, we derive different categories of exact solutions, like hyperbolic, trigonometric, and rational functions. The beta fractional derivative is used here to generalize the classical idea of the derivative, which preserves important principles. The derived solutions with broader nonlinear wave structures are periodic waves, breathers, peakons, W-shaped solitons, and singular solitons, which enhance our understanding of nonlinear wave dynamics. In relation to these results, the findings are described by showing the solitons’ physical behaviors, their stabilities, and dispersions under fractional parameters in the form of contour plots and 2D and 3D graphs. Comparisons with earlier studies underscore the originality and consistency of the (G′/G, 1/G)-expansion approach in addressing fractional-order evolution equations. It contributes new solutions to analytical problems of fractional nonlinear integrable systems and helps understand the systems’ dynamic behavior in a wider scope of applications. Full article
(This article belongs to the Special Issue Recent Computational Methods for Fractal and Fractional Nonlinear Partial Differential Equations)
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13 pages, 2314 KiB  
Article
A Novel Approach to Solving Fractional Navier–Stokes Equations Using the Elzaki Transform
by Tarig M. Elzaki and Eltaib M. Abd Elmohmoud
Fractal Fract. 2025, 9(6), 396; https://doi.org/10.3390/fractalfract9060396 - 19 Jun 2025
Viewed by 492
Abstract
A clear method is provided to explain a new approach for solving systems of fractional Navier–Stokes equations (SFNSEs) using initial conditions (ICs) that rely on the Elzaki transform (ET). A few steps show the technique’s validity and utility for handling SFNSE solutions. For [...] Read more.
A clear method is provided to explain a new approach for solving systems of fractional Navier–Stokes equations (SFNSEs) using initial conditions (ICs) that rely on the Elzaki transform (ET). A few steps show the technique’s validity and utility for handling SFNSE solutions. For fractional derivatives, the Caputo sense is used. This method does not need discretization or limiting assumptions and may be used to solve both linear and nonlinear SFNSEs. By eliminating round-off mistakes, the technique reduces the need for numerical calculations. Using examples, the new technique’s accuracy and efficacy are illustrated. Full article
(This article belongs to the Special Issue Recent Computational Methods for Fractal and Fractional Nonlinear Partial Differential Equations)
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