Journal ArticleDOI
A new collection of real world applications of fractional calculus in science and engineering
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
More filters
Journal ArticleDOI
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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
More filters
Journal ArticleDOI
Abundant bursting patterns of a fractional-order Morris–Lecar neuron model
Min Shi,Zaihua Wang +1 more
TL;DR: It is shown that the fractional-order derivative can activate the slow potassium ion channel faster and play an important role to modulate the firing activity of the new model.
Journal ArticleDOI
Fractional Diffusion Equation and the Electrical Impedance: Experimental Evidence in Liquid-Crystalline Cells
TL;DR: In this article, the electrical impedance data of different nematic liquid-crystal cells are analyzed in the framework of a model in which the diffusion of mobile ions in the bulk is governed by a fractional diffusion equation of distributed order.
Journal ArticleDOI
Fractional description of time-dependent mechanical property evolution in materials with strain softening behavior
TL;DR: In this paper, a variable order fractional viscoelastic model is presented to represent the time-dependent evolution of mechanical property including strain softening behaviors, which is applied to analyze the constant strain rate tension and compression tests in ductile metals and soils.
Journal ArticleDOI
Long and Short Memory in Economics: Fractional-Order Difference and Differentiation
TL;DR: In this article, it was shown that the long and short memory with power law should be described by exact fractional-order differences, for which the Fourier transform demonstrates the power law exactly.
Journal ArticleDOI
Fractional-order positive position feedback compensator for active vibration control of a smart composite plate
TL;DR: In this paper, a fractional-order Positive Position Feedback (PPF) compensator is proposed, implemented and compared to the standard integer-order PPF, which is found to be more efficient in achieving the same performance with less actuation voltage.