Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.6
3.6
Journals
Fractal Fract
Special Issues
Fractional Order Systems: Deterministic and Stochastic Analysis
share announcement

Fractional Order Systems: Deterministic and Stochastic Analysis

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

Deadline for manuscript submissions: closed (31 March 2021) | Viewed by 14270

Special Issue Editor

Prof. Dr. Amar Debbouche

E-Mail Website
Guest Editor
Department of Mathematics, Guelma University, Guelma 24000, Algeria
Interests: abstract differential equations; fractional calculus; control theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The field of fractional dynamic systems has become very popular and already attracted much scientists and research groups from around the world. Its main advantage is in modeling several complex phenomena, with the best results, in numerous seemingly diverse and widespread areas of science and engineering. Since such developments are currently considered essential in applied sciences, it is very important to focus on possible novelties of the most promising new directions and open problems that have been formulated based on modern techniques and approaches indicated in the latest scientific achievements.  

On the other side, the theory of stochastic processes is considered to be an important contribution to probability theory and continues to be an active topic of research for both theoretical reasons and applications. The word “stochastic” is used to describe other terms and objects in mathematics. Examples include a stochastic matrix, which describes a stochastic process known as a Markov process, and stochastic calculus, which involves differential equations and integrals based on stochastic processes such as the Wiener process, also called the Brownian motion process.

We strictly invite, via this open call for papers, strong interesting contributions providing original results which have been obtained from modern computational techniques of theoretical, experimental, and applied aspects of both deterministic and stochastic fractional dynamic systems. We also strongly encourage young researchers/PhD students who have achieved exciting results while supervised and guided by their scientific advisors to submit their works to this Special Issue. It is necessary that papers have to have a high-level mathematical ground. Note that submitted papers should explicitly meet the Aims and Scope of the FractalFract journal.

Topics to be included are:

  • Appropriate fractional derivative senses in applied sciences;
  • Computational methods for fractional dynamical systems;
  • Fractional inverse problems: modeling and simulation;
  • Cancer dynamic fractional systems: optimality and modeling;
  • Optimal control for fractional models of HIV/AIDS infection;
  • Latest advancements on COVID-19 pandemic fractional systems;
  • Continuous and discrete fractional systems with randomness;
  • Uncertainty quantification for random fractional dynamic systems;
  • Stochastic analysis for fractional mathematical models;
  • Instantaneous impulsive fractional equations and inclusions;
  • Applications of fractional problems in science and engineering;
  • Implementation methods and simulations for fractional models;
  • Fractional reaction-diffusion and Navier–Stokes equations;
  • Automorphic and periodic solutions for fractional systems;
  • Approximation methods for fractional order systems;
  • Stochastic processes involving fractional PDEs;
  • Control and optimization for fractional systems;
  • Variable order differentiation and integration;
  • Heat transfer involving local fractional operators;
  • Waves, wavelets and fractal: fractional calculus approach.

Prof. Dr. Amar Debbouche
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. 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.

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.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (5 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

16 pages, 378 KiB  
Article
Monotone Iterative Method for ψ-Caputo Fractional Differential Equation with Nonlinear Boundary Conditions
by Zidane Baitiche, Choukri Derbazi, Jehad Alzabut, Mohammad Esmael Samei, Mohammed K. A. Kaabar and Zailan Siri
Fractal Fract. 2021, 5(3), 81; https://doi.org/10.3390/fractalfract5030081 - 29 Jul 2021
Cited by 38 | Viewed by 2827
Abstract
The main contribution of this paper is to prove the existence of extremal solutions for a novel class of ψ-Caputo fractional differential equation with nonlinear boundary conditions. For this purpose, we utilize the well-known monotone iterative technique together with the method of [...] Read more.
The main contribution of this paper is to prove the existence of extremal solutions for a novel class of ψ-Caputo fractional differential equation with nonlinear boundary conditions. For this purpose, we utilize the well-known monotone iterative technique together with the method of upper and lower solutions. Finally, we provide an example along with graphical representations to confirm the validity of our main results. Full article
(This article belongs to the Special Issue Fractional Order Systems: Deterministic and Stochastic Analysis)
►▼ Show Figures

Figure 1

18 pages, 4605 KiB  
Article
Uncertainty Quantification of Random Microbial Growth in a Competitive Environment via Probability Density Functions
by Vicente José Bevia, Clara Burgos Simón, Juan Carlos Cortés and Rafael J. Villanueva Micó
Fractal Fract. 2021, 5(2), 26; https://doi.org/10.3390/fractalfract5020026 - 24 Mar 2021
Cited by 4 | Viewed by 2934
Abstract
The Baranyi–Roberts model describes the dynamics of the volumetric densities of two interacting cell populations. We randomize this model by considering that the initial conditions are random variables whose distributions are determined by using sample data and the principle of maximum entropy. Subsequenly, [...] Read more.
The Baranyi–Roberts model describes the dynamics of the volumetric densities of two interacting cell populations. We randomize this model by considering that the initial conditions are random variables whose distributions are determined by using sample data and the principle of maximum entropy. Subsequenly, we obtain the Liouville–Gibbs partial differential equation for the probability density function of the two-dimensional solution stochastic process. Because the exact solution of this equation is unaffordable, we use a finite volume scheme to numerically approximate the aforementioned probability density function. From this key information, we design an optimization procedure in order to determine the best growth rates of the Baranyi–Roberts model, so that the expectation of the numerical solution is as close as possible to the sample data. The results evidence good fitting that allows for performing reliable predictions. Full article
(This article belongs to the Special Issue Fractional Order Systems: Deterministic and Stochastic Analysis)
►▼ Show Figures

Figure 1

14 pages, 332 KiB  
Article
On Strongly Continuous Resolving Families of Operators for Fractional Distributed Order Equations
by Vladimir E. Fedorov and Nikolay V. Filin
Fractal Fract. 2021, 5(1), 20; https://doi.org/10.3390/fractalfract5010020 - 2 Mar 2021
Cited by 12 | Viewed by 2039
Abstract
The aim of this work is to find by the methods of the Laplace transform the conditions for the existence of a strongly continuous resolving family of operators for a linear homogeneous equation in a Banach space with the distributed Gerasimov–Caputo fractional derivative [...] Read more.
The aim of this work is to find by the methods of the Laplace transform the conditions for the existence of a strongly continuous resolving family of operators for a linear homogeneous equation in a Banach space with the distributed Gerasimov–Caputo fractional derivative and with a closed densely defined operator A in the right-hand side. It is proved that the existence of a resolving family of operators for such equation implies the belonging of the operator A to the class CW(K,a), which is defined here. It is also shown that from the continuity of a resolving family of operators at t=0 the boundedness of A follows. The existence of a resolving family is shown for A∈CW(K,a) and for the upper limit of the integration in the distributed derivative not greater than 2. As corollary, we obtain the existence of a unique solution for the Cauchy problem to the equation of such class. These results are used for the investigation of the initial boundary value problems unique solvability for a class of partial differential equations of the distributed order with respect to time. Full article
(This article belongs to the Special Issue Fractional Order Systems: Deterministic and Stochastic Analysis)
21 pages, 1026 KiB  
Article
Novel Techniques for a Verified Simulation of Fractional-Order Differential Equations
by Andreas Rauh and Luc Jaulin
Fractal Fract. 2021, 5(1), 17; https://doi.org/10.3390/fractalfract5010017 - 21 Feb 2021
Cited by 11 | Viewed by 2396
Abstract
Verified simulation techniques have been investigated intensively by researchers who are dealing with ordinary and partial differential equations. Tasks that have been considered in this context are the solution to initial value problems and boundary value problems, parameter identification, as well as the [...] Read more.
Verified simulation techniques have been investigated intensively by researchers who are dealing with ordinary and partial differential equations. Tasks that have been considered in this context are the solution to initial value problems and boundary value problems, parameter identification, as well as the solution of optimal control problems in cases in which bounded uncertainty in parameters and initial conditions are present. In contrast to system models with integer-order derivatives, fractional-order models have not yet gained the same attention if verified solution techniques are desired. In general, verified simulation techniques rely on interval methods, zonotopes, or Taylor model arithmetic and allow for computing guaranteed outer enclosures of the sets of solutions. As such, not only the influence of uncertain but bounded parameters can be accounted for in a guaranteed way. In addition, also round-off and (temporal) truncation errors that inevitably occur in numerical software implementations can be considered in a rigorous manner. This paper presents novel iterative and series-based solution approaches for the case of initial value problems to fractional-order system models, which will form the basic building block for implementing state estimation schemes in continuous-discrete settings, where the system dynamics is assumed as being continuous but measurements are only available at specific discrete sampling instants. Full article
(This article belongs to the Special Issue Fractional Order Systems: Deterministic and Stochastic Analysis)
►▼ Show Figures

Figure 1

13 pages, 281 KiB  
Article
Non-Linear First-Order Differential Boundary Problems with Multipoint and Integral Conditions
by Misir J. Mardanov, Yagub A. Sharifov, Yusif S. Gasimov and Carlo Cattani
Fractal Fract. 2021, 5(1), 15; https://doi.org/10.3390/fractalfract5010015 - 5 Feb 2021
Cited by 16 | Viewed by 2603
Abstract
This paper considers boundary value problem (BVP) for nonlinear first-order differential problems with multipoint and integral boundary conditions. A suitable Green function was constructed for the first time in order to reduce this problem into a corresponding integral equation. So that by using [...] Read more.
This paper considers boundary value problem (BVP) for nonlinear first-order differential problems with multipoint and integral boundary conditions. A suitable Green function was constructed for the first time in order to reduce this problem into a corresponding integral equation. So that by using the Banach contraction mapping principle (BCMP) and Schaefer’s fixed point theorem (SFPT) on the integral equation, we can show that the solution of the multipoint problem exists and it is unique. Full article
(This article belongs to the Special Issue Fractional Order Systems: Deterministic and Stochastic Analysis)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-5
Back to TopTop