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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Analytical and Integrative Aspects of the Stress-Strain-Time Problem
TL;DR: In this article, two ways in which the behavior of a complex body may be expressed in terms of the Hookean and Newtonian prototypes are discussed: the analytical approach regards the material as a physical mixture of ideal Hookeans and Newtonians components whereas the integrative view considers the behaviour as intermediate, molecular conditions being regarded as too complex to justify the useful construction of idealised models.
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Analytical and numerical study of electroosmotic slip flows of fractional second grade fluids
TL;DR: This work investigates the unsteady electroosmotic slip flow of viscoelastic fluid through a parallel plate micro-channel under combined influence of electroOSmotic and pressure gradient forcings with asymmetric zeta potentials at the walls.
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Tempered fractional Feynman-Kac equation: Theory and examples.
TL;DR: This paper focuses on deriving the forward and backward fractional Feynman-Kac equations describing the distribution of the functionals of the space and time-tempered anomalous diffusion, belonging to the continuous time random walk class.
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Grünwald–Letnikov operators for fractional relaxation in Havriliak–Negami models ☆
TL;DR: This work introduces new integral and differential operators for the description of Havriliak–Negami models in the time-domain and proposes a formulation of Grunwald–Letnikov type which turns out to be effective not only to provide a theoretical characterization of the operators associated to HavRiliak-Negami systems but also for computational purposes.
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Finite-time stability of discrete fractional delay systems: Gronwall inequality and stability criterion
TL;DR: Finite-time stability of Caputo delta fractional difference equations is investigated using a generalized Gronwall inequality on a finite time domain and finite-time stable conditions are provided.