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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Differentiating low- and high-grade pediatric brain tumors using a continuous-time random-walk diffusion model at high b-values.
TL;DR: It is shown that a continuous‐time random‐walk (CTRW) diffusion model can improve diagnostic accuracy of differentiating low‐ and high‐grade pediatric brain tumors.
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Dominant pole placement with fractional order PID controllers: D-decomposition approach
TL;DR: The design method presented in this paper tunes the parameters of PID and fractional PID controller in order to obtain good load disturbance response with a constraint on the maximum sensitivity and sensitivity to noise measurement.
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Understanding partial bed-load transport: Experiments and stochastic model analysis
TL;DR: In this article, the complex dynamics of partial bed-load transport in a series of well-controlled laboratory experiments are explored systematically and simulated by a stochastic model in a study.
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Spectral Capacitance of Series and Parallel Combinations of Supercapacitors
TL;DR: In this paper, a detailed impedance spectroscopy study of all possible series and parallel combinations of two different commercial 1 Farad carbon-carbon supercapacitors was performed, showing that these nominal DC capacitances are not suitable to evaluate the equivalent capacitance.
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A space fractional constitutive equation model for non-Newtonian fluid flow
TL;DR: A left-side, Caputo type, space fractional-order constitutive equation (FCE) is reported using a nonlocal, fractional velocity gradient and then interprets physical properties of non-Newtonian fluids for steady pipe flow and leads to analytical tools and criterion that can extend standard models in quantifying the complex dynamics ofnon- newtonian fluid flow.