Journal ArticleDOI
A new collection of real world applications of fractional calculus in science and engineering
Reads0
Chats0
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
Mathematical models of cell colonization of uniformly growing domains.
TL;DR: These models provide an insight into cell migration during embryonic growth, and its dependence upon the form and timing of the domain growth.
Journal ArticleDOI
Diffusion of cosmic rays in the expanding universe. I
V. Berezinsky,A. Gazizov +1 more
TL;DR: In this paper, an analytic solution of the diffusion equation for high-energy cosmic rays in the expanding universe is presented, where the particles are assumed to be ultrarelativistic, and they can have energy losses arbitrarily dependent on energy and time.
Journal ArticleDOI
An equivalence between generalized Maxwell model and fractional Zener model
Rui Xiao,HongGuang Sun,Wen Chen +2 more
TL;DR: In this paper, a detailed comparison of the performance of the generalized Maxwell model and fractional Zener model is presented, and the two models are then applied to investigate the stress response under constant strain rate, stress relaxation, cyclic and random loading conditions.
Journal ArticleDOI
Continuous fractional-order grey model and electricity prediction research based on the observation error feedback
Yang Yang,Yang Yang,Dingyü Xue +2 more
TL;DR: The generalized fractional-order forms for grey models are given, which could have more freedom and better modeling by the fractional derivatives and enrich the content, scope and application of grey theory.
Journal Article
A Class of Fractional-Order Variational Image Inpainting Models
TL;DR: This paper proposes a new class of fractional-order variational image inpainting models, in both space and wavelet domains, inspired by the works of Bai and Feng, and demonstrates better in painting performance on some image details than original integral-order inPainting based on classic calculus.