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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Book
Fractional Calculus: An Introduction for Physicists
TL;DR: In this article, the Fractional Derivative Friction Factorization Symmetries (FDFS) is used to describe the properties of a fractional spin.
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Molecular Modeling of the Volumetric and Thermodynamic Properties of Kerogen: Influence of Organic Type and Maturity
TL;DR: In this paper, the heat capacity in the ideal gas state is predicted to increase as a function of temperature, as obtained from quantum mechanics at the semi-empirical level (MOPAC-PM7).
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Measuring memory with the order of fractional derivative
Maolin Du,Zaihua Wang,Haiyan Hu +2 more
TL;DR: With the numerical least square method, it is shown that the fractional model perfectly fits the test data of memory phenomena in different disciplines, not only in mechanics, but also in biology and psychology.
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On fractional thermoelasticity
TL;DR: In this article, two general models of fractional heat conduction for non-homogeneous anisotropic elastic solids are introduced and the constitutive equations for thermoelasticity theory are obtained.
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Memory effect in a lithium-ion battery
TL;DR: A memory effect in LiFePO4, one of the materials used for the positive electrode in Li-ion batteries, appears already after only one cycle of partial charge and discharge and its connection to the particle-by-particle charge/discharge model is described.