Journal ArticleDOI
A new collection of real world applications of fractional calculus in science and engineering
TLDR
This review article aims to present some short summaries written by distinguished researchers in the field of fractional calculus that will guide young researchers and help newcomers to see some of the main real-world applications and gain an understanding of this powerful mathematical tool.About:
This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2018-11-01. It has received 922 citations till now.read more
Citations
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Journal ArticleDOI
A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator
TL;DR: Simulation results show that the new presented model based on the fractional operator with Mittag-Leffler kernel represents various asymptomatic behaviors that tracks the real data more accurately than the other fractional- and integer-order models.
Journal ArticleDOI
New variable-order fractional chaotic systems for fast image encryption.
TL;DR: The proposed new variable-order fractional chaotic systems improves security of the image encryption and saves the encryption time greatly.
Journal ArticleDOI
On a Fractional Operator Combining Proportional and Classical Differintegrals
TL;DR: The Caputo fractional derivative has been one of the most useful operators for modelling non-local behaviors by fractional differential equations as discussed by the authors. But it is not a suitable operator for modeling the Mittag-Leffler function.
Journal ArticleDOI
On Fractional Operators and Their Classifications
Dumitru Baleanu,Arran Fernandez +1 more
TL;DR: Fractional calculus dates its inception to a correspondence between Leibniz and L’Hopital in 1695 as discussed by the authors, and it has become a thriving field of research not only in mathematics but also in other parts of science such as physics, biology, and engineering.
Journal ArticleDOI
Review of fractional-order electrical characterization of supercapacitors
Anis Allagui,Anis Allagui,Todd J. Freeborn,Ahmed S. Elwakil,Ahmed S. Elwakil,Ahmed S. Elwakil,Mohammed E. Fouda,Mohammed E. Fouda,Brent Maundy,Ahmad G. Radwan,Ahmad G. Radwan,Zafar Said,Zafar Said,Mohammad Ali Abdelkareem,Mohammad Ali Abdelkareem,Mohammad Ali Abdelkareem +15 more
TL;DR: This review article is an attempt to present and discuss the main differences between ideal capacitors and supercapacitors, and especially how the performance metrics of the latter depend on the operating frequency, the charging/discharging waveform type as well as their deviation from ideality.
References
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Journal ArticleDOI
D-decomposition technique for stabilization of Furuta pendulum: fractional approach
TL;DR: In this article, a mathematical model of rotational inverted pendulum is derived and the fractional order PD controller is introduced in order to stabilize the same closed loop system using the D-decomposition approach.
Posted Content
A framework to investigate the immittance responses for finite length-situations: fractional diffusion equation, reaction term, and boundary conditions
Ervin K. Lenzi,Marcelo Kaminski Lenzi,Fernanda R. G. B. Silva,Giane Gonçalves,R. Rossato,Rafael S. Zola,Luiz Roberto Evangelista +6 more
TL;DR: In this paper, the authors extended the Poisson-Nernst-Planck (PNP) diffusional model for the immittance or impedance spectroscopy response of an electrolytic cell in a finite-length situation.
Proceedings ArticleDOI
A physical experimental study of the fractional harmonic oscillator
Gary Bohannan,Brenda Knauber +1 more
TL;DR: In both the transient and steady state cases, the Riemann-Liouville form proved to accurately model the system dynamics and demonstrated that undergraduates learned the fundamental concepts of fractional calculus quite readily.
Journal ArticleDOI
Modified grey model predictor design using optimal fractional-order accumulation calculus
Yang Yang,Dingyu Xue +1 more
TL;DR: The residual sequence represented by Fourier series is used to ameliorate performance of the fractionalorder accumulation GM U+0028 1, 1 U-0029 and improve the accuracy of predictor and illustrated that the fractiona-order calculus could be used to depict the GM precisely with more degrees of freedom.
Journal ArticleDOI
A fractional model for time-variant non-newtonian flow
TL;DR: In this article, the authors apply a fractional flow model to describe a time-variant behavior of non-Newtonian substances, and investigate the behaviors of cellulose suspensions and pastes under constant shear rate.