Stability, Periodicity, and Related Problems in Fractional-Order Systems
1
Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, 842 48 Bratislava, Slovakia
2
Mathematical Institute of Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia
3
STAR-UBB Institute, Babes-Bolyai University, 400084 Cluj-Napoca, Romania
4
Romanian Institute of Science and Technology, 400487 Cluj-Napoca, Romania
*
Author to whom correspondence should be addressed.
Mathematics 2022, 10(12), 2040; https://doi.org/10.3390/math10122040
Submission received: 2 June 2022
/
Accepted: 7 June 2022
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Published: 12 June 2022
(This article belongs to the Special Issue Stability, Periodicity, and Related Problems in Fractional-Order Systems)
Abstract
:This Special Issue aims to collect new perspectives on the trends in both theory and applications of stability of fractional order continuous and discrete systems, analytical and numerical approaches, and any related problems regarding (but not limited to) time-delayed systems and impulsive systems in all fields of science, as well as engineering and multidisciplinary applications.
MSC:
37N30; 34K37; 26A33This paper contains the submissions [1,2,3,4,5] invited to a Special Issue of Mathematics on “Stability, Periodicity, and Related Problems in Fractional-Order Systems”.
Fractional-order systems (FOSs), which are said to have fractional dynamics, are modeled by differential equations with non-integer derivatives. Integrals and derivatives of fractional orders illustrate objects with power-law nonlocality, power-law long-range dependence (time history), or fractal properties. FOSs are used to study behavior in nonlinear chaotic systems in electrochemistry, biology, viscoelasticity, physics, etc.
The response to our call for this Special Issue resulted in the following statistics for both published and rejected items: 12 total submissions, of which 5 research articles were published (41.66%), and 7 were rejected (58.3%).
The technical topics covered in the five articles published in this book include:
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- The existence and uniqueness of solutions for a nonlinear coupled system of Liouville–Caputo-type fractional integrodifferential equations supplemented with non-local discrete and integral boundary conditions [1] for a coupled system of ψ-Caputo hybrid fractional derivatives of the order of 1 < υ ≤ 2 subjected to Dirichlet boundary conditions [2].
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- A study of a class of a coupled system of fractional integrodifferential equations in the frame of Hilfer fractional derivatives with respect to another function [3].
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- A study of a system of coupled discrete fractional-order logistic maps, modeled by Caputo’s delta fractional difference in terms of its numerical integration and chaotic dynamics [4].
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- An existence theorem for a unique solution to the fuzzy fractional Volterra–Fredholm integrodifferential equations (FCFVFIDEs) to our result involving the Caputo derivative [5].
We found that the paper selections for this book were very inspiring and rewarding. We also thank the editorial staff and reviewers for their efforts and help during the process.
Author Contributions
All authors have read and agreed to the published version of the manuscript.
Funding
M.F. is partially supported by the Slovak Research and Development Agency under the contract No. APVV-18-0308 and by the Slovak Grant Agency VEGA No. 1/0358/20 and No. 2/0127/20.
Conflicts of Interest
The authors declare no conflict of interest.
References
- Humaira; Sarwar, M.; Abdeljawad, T.; Mlaiki, N. Fixed Point Results via Least Upper Bound Property and Its Applications to Fuzzy Caputo Fractional Volterra–Fredholm Integro-Differential Equations. Mathematics 2021, 9, 1969. [Google Scholar] [CrossRef]
- Danca, M.; Fečkan, M.; Kuznetsov, N.; Chen, G. Coupled Discrete Fractional-Order Logistic Maps. Mathematics 2021, 9, 2204. [Google Scholar] [CrossRef]
- Saeed, A.; Abdo, M.; Jeelani, M. Existence and Ulam–Hyers Stability of a Fractional-Order Coupled System in the Frame of Generalized Hilfer Derivatives. Mathematics 2021, 9, 2543. [Google Scholar] [CrossRef]
- Awadalla, M.; Abuasbeh, K.; Subramanian, M.; Manigandan, M. On a System of ψ-Caputo Hybrid Fractional Differential Equations with Dirichlet Boundary Conditions. Mathematics 2022, 10, 1681. [Google Scholar] [CrossRef]
- Subramanian, M.; Alzabut, J.; Abbas, M.; Thaiprayoon, C.; Sudsutad, W. Existence of Solutions for Coupled Higher-Order Fractional Integro-Differential Equations with Nonlocal Integral and Multi-Point Boundary Conditions Depending on Lower-Order Fractional Derivatives and Integrals. Mathematics 2022, 10, 1823. [Google Scholar] [CrossRef]
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MDPI and ACS Style
Fečkan, M.; Danca, M.-F. Stability, Periodicity, and Related Problems in Fractional-Order Systems. Mathematics 2022, 10, 2040. https://doi.org/10.3390/math10122040
AMA Style
Fečkan M, Danca M-F. Stability, Periodicity, and Related Problems in Fractional-Order Systems. Mathematics. 2022; 10(12):2040. https://doi.org/10.3390/math10122040
Chicago/Turabian StyleFečkan, Michal, and Marius-F. Danca. 2022. "Stability, Periodicity, and Related Problems in Fractional-Order Systems" Mathematics 10, no. 12: 2040. https://doi.org/10.3390/math10122040
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