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.
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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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Fractional Differential Analysis for Texture of Digital Image
PU Yi-Fei,PU Yi-Fei +1 more
TL;DR: In this paper, the capabilities of the fractional differential approach for the detection of textural features in two-dimensional digital images and the involved Lateral Inhibition Principle, were discussed.
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Anomalous-diffusion approach applied to the electrical response of water
TL;DR: The use of a fractional diffusion equation of distributed order with the interfaces governed by integrodifferential equations evidences the presence of anomalous diffusion due to the surface effects in Milli-Q deionized water.
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Numerical algorithms to estimate relaxation parameters and Caputo fractional derivative for a fractional thermal wave model in spherical composite medium
Bo Yu,Xiaoyun Jiang,Chu Wang +2 more
TL;DR: The results show that the proposed fractional thermal wave model is efficient and accurate in modeling the heat transfer in the hyperthermia experiment, and the proposed numerical method for simultaneously estimating multiple parameters for the fractional Thermal wave model in a spherical composite medium is effective.
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A fast adaptive reweighted residual-feedback iterative algorithm for fractional-order total variation regularized multiplicative noise removal of partly-textured images
Jun Zhang,Zhihui Wei,Liang Xiao +2 more
TL;DR: A simple reweighted residual-feedback iterative algorithm which provides a general framework to solve the fractional-order total variation regularized models with different fidelity terms and an adaptive RRFI algorithm for multiplicative noise removal is introduced.
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A time fractional convection–diffusion equation to model gas transport through heterogeneous soil and gas reservoirs
TL;DR: In this paper, the authors reviewed previous gas transport experiments conducted in laboratory columns and realworld oil-gas reservoirs and found that gas dynamics exhibit typical sub-diffusive behavior characterized by heavy late-time tailing in the gas breakthrough curves (BTCs), which cannot be effectively captured by classical transport models.