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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Mean exit time and escape probability for the anomalous processes with the tempered power-law waiting times
TL;DR: In this paper, the authors derived the nonlocal elliptic partial differential equations (PDEs) governing the mean first exit time and escape probability for the anomalous processes having the tempered Levy stable waiting times with the tempering index $\lambda>0$ and the stability index $0<\alpha \le 1$; as for the distribution of jump lengths or the type of the noises driving the system, two cases are considered, i.e., Gaussian white noise and non-Gaussian (tempered) $\beta$-stable ($0 <\beta<2$)
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Fractional-order integral resonant control of collocated smart structures
TL;DR: In this article, a fractional-order integral controller (FI) is proposed to improve the robustness of the closed-loop system to changes in the mass of the payload at the tip.
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Low-voltage commercial super-capacitor response to periodic linear-with-time current excitation: a case study
Ahmed S. Elwakil,Ahmed G. Radwan,Todd J. Freeborn,Anis Allagui,B. J. Maundy,Mohamed E. Fouda +5 more
TL;DR: The response of a commercial super-capacitor to an applied periodic current excitation in the form of a triangular waveform has a linear-with-time variation which enables linear charging and discharging of the device.
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Self-similarity principle: the reduced description of randomness
TL;DR: In this article, a new general fitting method based on the Self-Similar (SS) organization of random sequences is presented, which helps to fit the response of many complex systems when their recorded data form a self-similar curve.
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Optimal random search, fractional dynamics and fractional calculus
Caibin Zeng,YangQuan Chen +1 more
TL;DR: The Continuous Time Random Walk (CTRW) optimal search framework is proposed and its master equation is derived from fractional calculus technique to show the mechanism of such complex fractional dynamics.