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Fractal Fract
Special Issues
Deterministic and Stochastic Fractional Differential Systems
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Deterministic and Stochastic Fractional Differential Systems

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".

Deadline for manuscript submissions: closed (27 August 2023) | Viewed by 5584

Special Issue Editors

Dr. Velusamy Vijayakumar

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Guest Editor
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, India
Interests: fractional calculus; mathematical control theory; stochastic systems; impulsive systems; neural networks
Special Issues, Collections and Topics in MDPI journals
Dr. Anurag Shukla

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Guest Editor
Department of Applied Sciences, Rajkiya Engineering College Kannauj, Kannauj 209732, India
Interests: mathematical control theory; differential equations; fractional calculus; dynamical systems
Dr. Muslim Malik

E-Mail Website
Guest Editor
School of Mathematical and Statistical Sciences, Indian Institutes of Technology Mandi, Kamand 175005, India
Interests: fractional differential equations; mathematical control theory; time scale problems and inverse problems

Special Issue Information

Dear Colleagues,

Fractional differential equations have lately emerged as a very significant area of research due to their continuously expanding number of applications in several areas of applied science and engineering. When compared to differential equations represented by traditional integer order derivatives, fractional order differential equations offer a more precise and plausible explanation for a range of physical phenomena. Because of environmental noise, which is random or at least appears to be, deterministic models frequently show fluctuations. Therefore, we must change deterministic conditions to stochastic ones. In order to take into account disturbances, the theory of differential equations has been broadened to incorporate a stochastic functional differential equation.

The focus of this Special Issue is to continue to advance research on topics relating to the theory and application of fractional-order deterministic and stochastic systems. Topics that are invited for submission include (but are not limited to):

  • Fractional deterministic and stochastic systems of orders (0,1) and (1,2);
  • Hilfer fractional deterministic and stochastic systems;
  • Atangana–Baleanu fractional deterministic and stochastic systems;
  • Fractal and fractional derivatives via fixed point techniques;
  • Solving fractional differential systems via measure of noncompactness;
  • Fractional differential systems with control theory;
  • Mathematical modelling with fractional order.

Dr. Velusamy Vijayakumar
Dr. Anurag Shukla
Dr. Muslim Malik
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.

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

Published Papers (3 papers)

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Research

24 pages, 425 KiB  
Article
An Analysis on the Optimal Control for Fractional Stochastic Delay Integrodifferential Systems of Order 1 < γ < 2
by Murugesan Johnson and Velusamy Vijayakumar
Fractal Fract. 2023, 7(4), 284; https://doi.org/10.3390/fractalfract7040284 - 25 Mar 2023
Cited by 12 | Viewed by 1201
Abstract
The purpose of this paper is to investigate the optimal control for fractional stochastic integrodifferential systems of order 1 < γ < 2. To ensure the existence and uniqueness of mild solutions, we first gather a novel list of requirements. Further, the existence [...] Read more.
The purpose of this paper is to investigate the optimal control for fractional stochastic integrodifferential systems of order 1 < γ < 2. To ensure the existence and uniqueness of mild solutions, we first gather a novel list of requirements. Further, the existence of optimal control for the stated issue is given by applying Balder’s theorem. Additionally, we extend our existence outcomes with infinite delay. The outcomes are obtained via fractional calculus, Hölder’s inequality, the cosine family, stochastic analysis techniques, and the fixed point approach. The theory is shown by an illustration, as well. Full article
(This article belongs to the Special Issue Deterministic and Stochastic Fractional Differential Systems)
10 pages, 295 KiB  
Article
Applications of the Neutrosophic Poisson Distribution for Bi-Univalent Functions Involving the Modified Caputo’s Derivative Operator
by S. Santhiya and K. Thilagavathi
Fractal Fract. 2023, 7(1), 35; https://doi.org/10.3390/fractalfract7010035 - 28 Dec 2022
Viewed by 1495
Abstract
This paper establishes the upper bounds for the second and third coefficients of holomorphic and bi-univalent functions in a family which involves Bazilevic functions and μ-pseudo-starlike functions under a new operator, joining the neutrosophic Poisson distribution with the modified Caputo’s derivative operator. [...] Read more.
This paper establishes the upper bounds for the second and third coefficients of holomorphic and bi-univalent functions in a family which involves Bazilevic functions and μ-pseudo-starlike functions under a new operator, joining the neutrosophic Poisson distribution with the modified Caputo’s derivative operator. We also discuss Fekete–Szego’s function problem in this family. Examples are given to support our case for the neutrosophic Poisson distribution. The fields of physics, mechanics, engineering, and biology all make extensive use of fractional derivatives. Full article
(This article belongs to the Special Issue Deterministic and Stochastic Fractional Differential Systems)
14 pages, 1010 KiB  
Article
Chaos Controllability in Fractional-Order Systems via Active Dual Combination–Combination Hybrid Synchronization Strategy
by Mohammad Sajid, Harindri Chaudhary, Ali Allahem and Santosh Kaushik
Fractal Fract. 2022, 6(12), 717; https://doi.org/10.3390/fractalfract6120717 - 2 Dec 2022
Cited by 8 | Viewed by 1568
Abstract
In this paper, the dual combination–combination hybrid synchronization (DCCHS) scheme has been investigated in fractional-order chaotic systems with a distinct dimension applying a scaling matrix. The formulations for the active control have been analyzed numerically using Lyapunov’s stability analysis in order to achieve [...] Read more.
In this paper, the dual combination–combination hybrid synchronization (DCCHS) scheme has been investigated in fractional-order chaotic systems with a distinct dimension applying a scaling matrix. The formulations for the active control have been analyzed numerically using Lyapunov’s stability analysis in order to achieve the proposed DCCHS among the considered systems. With the evolution of time, the error system then converges to zero by applying a suitably designed control function. The proposed synchronization technique depicts a higher degree of complexity in error systems, and therefore, the DCCHS scheme provides higher protection for secure communication. Mathematical simulations are implemented using MATLAB, the results of which confirm that the proposed approach is superior and more effective in comparison to existing chaos literature. Full article
(This article belongs to the Special Issue Deterministic and Stochastic Fractional Differential Systems)
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