Recent Advances in Fractional Order Elements with Applications

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

Deadline for manuscript submissions: closed (30 April 2023) | Viewed by 2041

Special Issue Editors


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Guest Editor
Department of Electrical Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India
Interests: fractional order element; device fabrication; instrumentation system design
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Guest Editor
Department of Electrical Engineering, Dr. B. C. Roy Engineering College, Durgapur 713206, West Bengal, India
Interests: analog electronics; signal processing; optimization; fractional-order filter; control theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Over the last two decades, researchers have shown enormous interest in the study of the fractional order system, as is evident from the exponentially growing number of publications in the field. The topic is quite advanced in the theoretical domain, with famous mathematicians having worked on developing fractional calculus and renowned scientists designing various circuits and specially designed fractional PID controllers. Many seminal works have rightly pointed out that fractional order system modeling and controllers are more effective than standard ones.

Unfortunately, we have still not achieved acceptance of the fractional controller/fractional circuits by the industry, nor has it been well adopted in undergraduate curricula. One of the main reasons for this may be the unavailability of a commercial fractional order element which can be readily used in the electronic laboratory like capacitors, resistors, or inductors are. In this perspective, the aim of the Special Issue is to give the opportunity to present existing and new devices. The issue will also focus on the advantages of fractional order circuits and systems realized with a fractional order element.

Dr. Riccardo Caponetto
Dr. Karabi Biswas
Dr. Shibendu Mahata
Guest Editors

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Keywords

  • fractional order circuits, digital and analogue
  • constant phase element realization and applications
  • application of fractional order elements
  • fractional PID controllers

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Published Papers (1 paper)

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Research

16 pages, 4564 KiB  
Article
Analytical Study of the Complexities in a Three Species Food Web Model with Modified Caputo–Fabrizio Operator
by Badr Saad T. Alkahtani
Fractal Fract. 2023, 7(2), 105; https://doi.org/10.3390/fractalfract7020105 - 18 Jan 2023
Cited by 2 | Viewed by 1417
Abstract
This article presents the analytical study of the three species fractional food web model in the framework of the Modified Caputo–Fabrizio operator. With the help of fixed point theory, the existence and uniqueness results are investigated for the fractional order model. To obtain [...] Read more.
This article presents the analytical study of the three species fractional food web model in the framework of the Modified Caputo–Fabrizio operator. With the help of fixed point theory, the existence and uniqueness results are investigated for the fractional order model. To obtain the approximate solution for the suggested model, the well-known Laplace–Adomian decomposition method is used. The solutions are validated through simulations with a variety of fractional orders and initial values, where the complex nature of the system can be observed. The technique used here can be easily used to study a range of complex problems in different branches of science. From the figures, it can be observed that, at integer higher fractional order, there are a number of oscillations in the system and the system behaves chaotically, while, at lower fractional orders, the oscillation amplitudes decrease, resulting in the faster converging towards the equilibrium point. According to the results, the Modified Caputo–Fabrizio fractional-order derivative may be used in a variety of future fractional dynamics scenarios. Full article
(This article belongs to the Special Issue Recent Advances in Fractional Order Elements with Applications)
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