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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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
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Proceedings ArticleDOI
Image Segmentation Based on Fractional Differentiation and RSF Model
TL;DR: The proposed method adds the global Grünwald-Letnikov fractional gradient into the RSF model and strengthens the gradient of the intensity inhomogeneity and weak texture regions, and both the robustness of initial location of evolution curve and efficiency of image segmentation are improved.
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An integrated fractional partial differential equation and molecular dynamics model of anomalously diffusive transport in heterogeneous nano-pore structures
TL;DR: An integrated fractional partial differential equation and molecular dynamics upscaling modeling of anomalously diffusive transport in heterogeneous nano-pore structures is developed, which has a significantly improved computational efficiency and memory requirement over the molecular dynamics simulation.
Proceedings ArticleDOI
Connecting the Viscous Grain-shearing Mechanism of Wave Propagation in Marine Sediments to Fractional Calculus
Vikash Pandey,Sverre Holm +1 more
TL;DR: In this paper, the authors build on Buckingham's viscous grain-shearing (VGS) model to explain wave propagation in saturated, unconsolidated granular materials and find that the material impulse response function derived from the VGS model is similar to the power-law memory kernel of fractional calculus.
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A Fractional-order Positive Position Feedback Compensator for Active Vibration Control
TL;DR: In this paper, a fractional-order positive position feedback compensator is proposed to overcome the limitations of the commonly used integer-order PPF such as: frequency spillover, amplitude amplification in the quasi-static region of the closed-loop response, and difficult tuning in multi-mode control.
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A Fractional-Order Level Set Model for Image Segmentation
Dan Tian,Xiaodan Zhang,Linan Fan +2 more