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Fractal Fract
Special Issues
General Fractional Calculus: Theory, Methods and Applications in Mathematical Physics
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Special Issue "General Fractional Calculus: Theory, Methods and Applications in Mathematical Physics"

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

Deadline for manuscript submissions: 31 January 2024 | Viewed by 1914

Special Issue Editors

Dr. Yi-Ying Feng
E-Mail Website
Guest Editor
School of Mathematics and Statistics, Suzhou University, Suzhou 234000, China
Interests: fractional calculus; local fractional calculus; general fractional calculus; creep constitutive model; applied mathematics; mechanical engineering
Dr. Jian-Gen Liu

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, China
Interests: fractional calculus; local fractional calculus; mathematical physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractional calculus can contain different fractional operators to obtain many fractional derivatives, and the generalisation is always a key concept in mathematics. Therefore, it is of utmost importance to study the general fractional calculus that enlarges the natural limitation of various definitions for fractional derivatives.

This subject matter of this Special Issue aims at highlighting the general fractional calculus to solve problems that affect foundational mathematical research and engineering technology. Many phenomena from physics, chemistry, mechanics and electricity can be modeled using differential equations involving general fractional derivatives. In addition, the research in the field of general fractional calculus is interdisciplinary. Its development can also promote the vigorous development of several fields. Topics that are invited for submission include (but are not limited to):

  • general fractional calculus theory;
  • general fractional calculus method;
  • general fractional calculus applications;
  • fractional viscoelasticity;
  • fractional dynamical systems;
  • fractional calculus in anomalous diffusion;
  • fractional operator theory and theoretical analysis;
  • new definitions and properties of general fractional calculus;
  • memory and heritability of general fractional calculus.

Dr. Yi-Ying Feng
Dr. Jian-Gen Liu
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

  • general fractional calculus theory
  • general fractional calculus method
  • general fractional calculus applications
  • fractional viscoelasticity
  • fractional dynamical systems
  • fractional calculus in anomalous diffusion
  • fractional operator theory and theoretical analysis
  • new definitions and properties of general fractional calculus
  • memory and heritability of general fractional calculus

Published Papers (3 papers)

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Article
Dynamic Compressive Mechanical Property Characteristics and Fractal Dimension Applications of Coal-Bearing Mudstone at Real-Time Temperatures
by
Shiru Guo
,
Lianying Zhang
,
Hai Pu
,
Yadong Zheng
,
Bing Li
,
Peng Wu
,
Peitao Qiu
,
Chao Ma
and
Yiying Feng
Fractal Fract. 2023, 7(9), 695; https://doi.org/10.3390/fractalfract7090695 - 18 Sep 2023
Viewed by 463
Abstract
Coal-bearing rocks are inevitably exposed to high temperatures and impacts (rapid dynamic load action) during deep-earth resource extraction, necessitating the study of their mechanical properties under such conditions. This paper reports on dynamic compression tests conducted on coal-bearing mudstone specimens at real-time temperatures [...] Read more.
Coal-bearing rocks are inevitably exposed to high temperatures and impacts (rapid dynamic load action) during deep-earth resource extraction, necessitating the study of their mechanical properties under such conditions. This paper reports on dynamic compression tests conducted on coal-bearing mudstone specimens at real-time temperatures (the temperature of the rock remains constant throughout the impact process) ranging from 25 °C to 400 °C using a temperature Hopkinson (T-SHPB) test apparatus developed in-house. The objective is to analyze the relationship between mechanical properties and the fractal dimension of fractured fragments and to explore the mechanical response of coal-bearing mudstone specimens to the combined effects of temperature and impact using macroscopic fracture characteristics. The study found that the peak stress and dynamic elastic modulus initially increased and then decreased with increasing temperature, increasing in the 25–150 °C range and monotonically decreasing in the 150–400 °C range. Based on the distribution coefficients and fractal dimensions of the fractured fragments, it was found that the degree of damage of coal-bearing mudstone shows a trend of an initial decrease and then an increase with increasing temperature. In the temperature range of 25–150 °C, the expansion of clay minerals within the mudstone filled the voids between the skeletal particles, resulting in densification and decreased damage. In the temperature range of 150–400 °C, thermal stresses increased the internal fractures and reduced the overall strength of the mudstone, resulting in increased damage. Negative correlations between fractal dimensions, the modulus of elasticity, and peak stress could be used to predict rock properties in engineering. Full article
(This article belongs to the Special Issue General Fractional Calculus: Theory, Methods and Applications in Mathematical Physics)
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Article
Two Integral Representations for the Relaxation Modulus of the Generalized Fractional Zener Model
by
Emilia Bazhlekova
and
Sergey Pshenichnov
Fractal Fract. 2023, 7(8), 636; https://doi.org/10.3390/fractalfract7080636 - 20 Aug 2023
Viewed by 419
Abstract
A class of generalized fractional Zener-type viscoelastic models with general fractional derivatives is considered. Two integral representations are derived for the corresponding relaxation modulus. The first representation is established by applying the Laplace transform to the constitutive equation and using the Bernstein functions [...] Read more.
A class of generalized fractional Zener-type viscoelastic models with general fractional derivatives is considered. Two integral representations are derived for the corresponding relaxation modulus. The first representation is established by applying the Laplace transform to the constitutive equation and using the Bernstein functions technique to justify the change of integration contour in the complex Laplace inversion formula. The second integral representation for the relaxation modulus is obtained by applying the subordination principle for the relaxation equation with generalized fractional derivatives. Two particular examples of the considered class of models are discussed in more detail: a model with fractional derivatives of uniformly distributed order and a model with general fractional derivatives, the kernel of which is a multinomial Mittag-Leffler-type function. To illustrate the analytical results, some numerical examples are presented. Full article
(This article belongs to the Special Issue General Fractional Calculus: Theory, Methods and Applications in Mathematical Physics)
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Article
Multiplicity of Positive Solutions to Hadamard-Type Fractional Relativistic Oscillator Equation with p-Laplacian Operator
by
Tengfei Shen
Fractal Fract. 2023, 7(6), 427; https://doi.org/10.3390/fractalfract7060427 - 25 May 2023
Viewed by 416
Abstract
The purpose of this paper is to investigate the initial value problem of Hadamard-type fractional relativistic oscillator equation with p-Laplacian operator. By overcoming the perturbation of singularity to fractional relativistic oscillator equation, the multiplicity of positive solutions to the problem were proved [...] Read more.
The purpose of this paper is to investigate the initial value problem of Hadamard-type fractional relativistic oscillator equation with p-Laplacian operator. By overcoming the perturbation of singularity to fractional relativistic oscillator equation, the multiplicity of positive solutions to the problem were proved via the methods of reducing and topological degree in cone, which extend and enrich some previous results. Full article
(This article belongs to the Special Issue General Fractional Calculus: Theory, Methods and Applications in Mathematical Physics)
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