Journal ArticleDOI
A new collection of real world applications of fractional calculus in science and engineering
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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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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.
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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.
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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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Book
Fractional Kinetics In Solids: Anomalous Charge Transport In Semiconductors, Dielectrics And Nanosystems
TL;DR: Anomalous Diffusion Dispersive Transport in Semiconductors Anomalous Dielectric Relaxation Quantum Dot Systems as discussed by the authors Theoretically, quantum dot systems can be considered a quantum dot system.
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A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising
Zhang Jun,Wei Zhihui +1 more
TL;DR: In this paper, the authors proposed a new space of functions of fractional-order bounded variation called the BV α space by using the Grunwald-Letnikov definition of fractiona-order derivative, which can improve the peak signal to noise ratio of image, preserve textures and eliminate the staircase effect.
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A causal and fractional all-frequency wave equation for lossy media
Sverre Holm,Sven Peter Näsholm +1 more
TL;DR: This work presents a lossy partial differential acoustic wave equation including fractional derivative terms derived from first principles of physics and an equation of state given by the fractional Zener stress-strain constitutive relation that is causal for all frequencies.
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On random walks and entropy in diffusion‐weighted magnetic resonance imaging studies of neural tissue
TL;DR: In diffusion‐weighted MRI studies of neural tissue, the classical model assumes the statistical mechanics of Brownian motion and predicts a monoexponential signal decay, but there have been numerous reports of signal decays that are not monoexp exponential, particularly in the white matter.
Book
Fractional Calculus View of Complexity : Tomorrow's Science
TL;DR: In this paper, the challenge of complexity in linear systems has been discussed and the fractional calculus has been used to control complexity of linear systems, including the size effect.