Emergent patterns in diffusive Turing-like systems with fractional-order operator

2021 ◽  
Author(s):  
Kolade M. Owolabi ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Order ◽  
Order Operator

scholarly journals Adaptive Fractional-Order Operator Clock Synchronization Algorithm Based on Grey Prediction

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Hongwei Yang ◽  
Long Wang ◽  
Jing Zhang ◽  
Li Li
Keyword(s):  
Fractional Order ◽  
Clock Synchronization ◽  
Sensor Nodes ◽  
Prediction Algorithm ◽  
Grey Prediction ◽  
Order Operator ◽  
Message Transmission ◽  
Synchronization Algorithm ◽  
Improved Stability ◽  
Clock Offset

As a result of the influence of clock drift and uncertainty delay in synchronous message transmission, the clock synchronization model based on statistical distribution cannot accurately describe clock deviation. This model also requires a large number of timestamp samples that cause a storage occupation issue for wireless sensor nodes with limited resources. The modeling method based on grey prediction has advantages of low sample demand and simple modeling process. However, the accuracy of the existing clock synchronization models needs to be improved. Based on the grey prediction theory, this paper proposes an adaptive fractional-order operator clock synchronization algorithm considering uncertainty delay. First, based on the clock model and clock offset model, the frequency offset between nodes is optimized by taking the mean on the clock frequencies. Second, a grey prediction algorithm based on a fractional-order operator is proposed by estimating the uncertainty delay in message transmission to obtain the clock offset. Finally, the order of the fractional-order accumulation is adjusted adaptively in the grey prediction model according to the collected timestamp sample values so that the estimation of the uncertainty delay is more accurate, thereby improving the accuracy of the clock offset. Compared with the first-order accumulative grey prediction clock synchronization algorithms and timing-sync protocol for sensor networks, the proposed scheme improved the synchronization accuracy by 29.18% and 44.01%, respectively, and reduced the variance of the clock offset by 48.66% and 64.89%. Thus, the proposed algorithm is characterized by improved stability.

A Fractional-order Sobel Operator for Medical Image Structure Feature Extraction

2013 ◽  
Vol 860-863 ◽  
pp. 2910-2913 ◽  
Author(s):  
Dan Tian ◽  
Jing Fei Wu ◽  
Ya Jie Yang
Keyword(s):  
Feature Extraction ◽  
Fractional Order ◽  
Medical Image ◽  
Order Operator ◽  
Visual Effects ◽  
Image Structure ◽  
First Order ◽  
Structure Feature ◽  
Sobel Operator ◽  
Edge Points

This paper proposes a novel fractional-order gradient operator for medical image structure feature extraction. The proposed operator can be seen as generalization of the first-order Sobel operator. The goal is to utilize the frequency characteristic of the fractional derivative for extracting more structure feature details. A thresholding is set based on the average fractional-order gradient for marking the edge points, and then the image structure can be extracted. Experiments show that the proposed fractional-order operator yields good visual effects.

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