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.
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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.
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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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Reduced fractional modeling of 3D video streams: the FERMA approach
TL;DR: A fractional exponential reduction moments approach based on the statistics of the so-called fractional moments that allow fitting to the sequence by exponential functions and then a characterization and classification of the video by a sort of fingerprint.
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Asymptotic behaviors of the Poisson-Nernst-Planck model, generalizations and best adjust of experimental data
Ervin K. Lenzi,Rafael S. Zola,R. Rossato,Haroldo V. Ribeiro,Denner S. Vieira,Luiz Roberto Evangelista +5 more
TL;DR: In this paper, the authors analyze the asymptotic behavior of the impedance (or immittance) spectroscopy response of an electrolytic cell in a finite-length situation obtained from the Poisson-Nernst-Planck (PNP) diffusional model and extensions by taking into account different surface effects.
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The finite difference method for Caputo-type parabolic equation with fractional Laplacian: more than one space dimension
Ye Hu,Changpin Li,Hefeng Li +2 more
TL;DR: The convergence and error estimate of the established finite difference scheme are shown and the illustrative examples are displayed which support the theoretical analysis.
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Upscaling chemical reactions in multicontinuum systems: When might time fractional equations work?
TL;DR: In this article, the authors consider a multicontinuum mobile-immobile system and demonstrate that an effective transport equation for a conserved scalar can be written that is similar to a diffusion equation but with an additional term that convolves a memory function and the time derivative term.
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An Efficient Variational Method for Restoring Images with Combined Additive and Multiplicative Noise
TL;DR: Wang et al. as mentioned in this paper proposed a novel variational model to remove additive or multiplicative noise from synthetic and natural digital images via the fractional-order derivative operator, which can help preserve textures and eliminate the blocky effect.