Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.7
2.7
Journals
Entropy
Special Issues
Fractional Calculus and Fractional Dynamics
entropy-logo
Submit to Entropy Review for Entropy Propose a Special Issue

Journal Menu

► Journal Menu

Journal Browser

► Journal Browser
share announcement

Fractional Calculus and Fractional Dynamics

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 2954

Special Issue Editor

Prof. Dr. Vasily E. Tarasov

E-Mail Website
Guest Editor
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
Interests: fractional calculus; fractional dynamics; mathematical economics; quantum theory; theoretical physics; processes with memory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractional calculus is a theory of differential and integral operators of arbitrary (integer and non-integer) orders that form a calculus, in which fractional generalizations of fundamental theorems are satisfied. Fractional derivatives and integrals of non-integer order are powerful mathematical tools used to describe complex processes with spatial non-locality, long memory, distributed lag, fractional spatial and frequency dispersion.

Fractional dynamics is an interdisciplinary science, in which processes with non-locality and memory are described by using fractional calculus. In the framework of fractional dynamics, complex physical, chemical, biological and social economic systems are studied using fractional calculus.

This Special Issue of the journal Entropy (MDPI) invites works on the use of rigorous and proven mathematical results of fractional calculus to describe different types of complex processes and systems. In this Special Issue of Entropy, works should be focused on problems of fractional calculus and its applications. Works devoted to the development and application of general fractional calculus, which is based on general fractional integrals and derivatives with Sonine kernels and its generalizations, are welcome.

Prof. Dr. Vasily E. Tarasov
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 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. Entropy 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 2600 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

  • fractional calculus
  • general fractional calculus
  • fractional derivatives
  • fractional integrals
  • fractional differential equations
  • fractional integral equations
  • fractional dynamics
  • spatial non-locality
  • long memory

Published Papers (3 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

19 pages, 4974 KiB  
Article
Complexity Synchronization of Organ Networks
by Bruce J. West, Paolo Grigolini, Scott E. Kerick, Piotr J. Franaszczuk and Korosh Mahmoodi
Entropy 2023, 25(10), 1393; https://doi.org/10.3390/e25101393 - 28 Sep 2023
Cited by 4 | Viewed by 1042
Abstract
The transdisciplinary nature of science as a whole became evident as the necessity for the complex nature of phenomena to explain social and life science, along with the physical sciences, blossomed into complexity theory and most recently into complexitysynchronization. This science motif is [...] Read more.
The transdisciplinary nature of science as a whole became evident as the necessity for the complex nature of phenomena to explain social and life science, along with the physical sciences, blossomed into complexity theory and most recently into complexitysynchronization. This science motif is based on the scaling arising from the 1/f-variability in complex dynamic networks and the need for a network of networks to exchange information internally during intra-network dynamics and externally during inter-network dynamics. The measure of complexity adopted herein is the multifractal dimension of the crucial event time series generated by an organ network, and the difference in the multifractal dimensions of two organ networks quantifies the relative complexity between interacting complex networks. Information flows from dynamic networks at a higher level of complexity to those at lower levels of complexity, as summarized in the ‘complexity matching effect’, and the flow is maximally efficient when the complexities are equal. Herein, we use the scaling of empirical datasets from the brain, cardiovascular and respiratory networks to support the hypothesis that complexity synchronization occurs between scaling indices or equivalently with the matching of the time dependencies of the networks’ multifractal dimensions. Full article
(This article belongs to the Special Issue Fractional Calculus and Fractional Dynamics)
►▼ Show Figures

Figure 1

18 pages, 333 KiB  
Article
Stability of Delay Hopfield Neural Networks with Generalized Riemann–Liouville Type Fractional Derivative
by Ravi P. Agarwal and Snezhana Hristova
Entropy 2023, 25(8), 1146; https://doi.org/10.3390/e25081146 - 31 Jul 2023
Viewed by 658
Abstract
The general delay Hopfield neural network is studied. We consider the case of time-varying delay, continuously distributed delays, time-varying coefficients, and a special type of a Riemann–Liouville fractional derivative (GRLFD) with an exponential kernel. The kernels of the fractional integral and the fractional [...] Read more.
The general delay Hopfield neural network is studied. We consider the case of time-varying delay, continuously distributed delays, time-varying coefficients, and a special type of a Riemann–Liouville fractional derivative (GRLFD) with an exponential kernel. The kernels of the fractional integral and the fractional derivative in this paper are Sonine kernels and satisfy the first and the second fundamental theorems in calculus. The presence of delays and GRLFD in the model require a special type of initial condition. The applied GRLFD also requires a special definition of the equilibrium of the model. A constant equilibrium of the model is defined. An inequality for Lyapunov type of convex functions with the applied GRLFD is proved. It is combined with the Razumikhin method to study stability properties of the equilibrium of the model. As a partial case we apply quadratic Lyapunov functions. We prove some comparison results for Lyapunov function connected deeply with the applied GRLFD and use them to obtain exponential bounds of the solutions. These bounds are satisfied for intervals excluding the initial time. Also, the convergence of any solution of the model to the equilibrium at infinity is proved. An example illustrating the importance of our theoretical results is also included. Full article
(This article belongs to the Special Issue Fractional Calculus and Fractional Dynamics)
45 pages, 515 KiB  
Article
General Nonlocal Probability of Arbitrary Order
by Vasily E. Tarasov
Entropy 2023, 25(6), 919; https://doi.org/10.3390/e25060919 - 10 Jun 2023
Cited by 4 | Viewed by 783
Abstract
Using the Luchko’s general fractional calculus (GFC) and its extension in the form of the multi-kernel general fractional calculus of arbitrary order (GFC of AO), a nonlocal generalization of probability is suggested. The nonlocal and general fractional (CF) extensions of probability density functions [...] Read more.
Using the Luchko’s general fractional calculus (GFC) and its extension in the form of the multi-kernel general fractional calculus of arbitrary order (GFC of AO), a nonlocal generalization of probability is suggested. The nonlocal and general fractional (CF) extensions of probability density functions (PDFs), cumulative distribution functions (CDFs) and probability are defined and its properties are described. Examples of general nonlocal probability distributions of AO are considered. An application of the multi-kernel GFC allows us to consider a wider class of operator kernels and a wider class of nonlocality in the probability theory. Full article
(This article belongs to the Special Issue Fractional Calculus and Fractional Dynamics)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-3
Back to TopTop