PARTIAL FRACTIONAL-ORDER DIFFERENCE IN THE EDGE DETECTION

2014 ◽  
pp. 139-157
Author(s):  
Piotr Duch ◽  
Rafał Jachowicz ◽  
Sylwester Błaszczyk ◽  
Maciej Łaski ◽  
Adam Wulkiewicz ◽  
...  
Keyword(s):  
Edge Detection ◽  
Fractional Order ◽  
Order Difference

scholarly journals Fractional-Order Colour Image Processing

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 457
Author(s):  
Manuel Henriques ◽  
Duarte Valério ◽  
Paulo Gordo ◽  
Rui Melicio
Keyword(s):  
Image Processing ◽  
Edge Detection ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Grey Scale ◽  
Colour Image ◽  
Colour Image Processing ◽  
Image Processing Algorithms ◽  
Processing Algorithms

Many image processing algorithms make use of derivatives. In such cases, fractional derivatives allow an extra degree of freedom, which can be used to obtain better results in applications such as edge detection. Published literature concentrates on grey-scale images; in this paper, algorithms of six fractional detectors for colour images are implemented, and their performance is illustrated. The algorithms are: Canny, Sobel, Roberts, Laplacian of Gaussian, CRONE, and fractional derivative.

scholarly journals Fractional Order Processing of Satellite Images

2021 ◽  
Vol 11 (11) ◽  
pp. 5288
Author(s):  
Manuel Henriques ◽  
Duarte Valério ◽  
Rui Melicio
Keyword(s):  
Edge Detection ◽  
Fractional Order ◽  
High Performance ◽  
Satellite Images ◽  
Automatic Detection ◽  
Automatic Processing ◽  
Order Processing ◽  
Detection Algorithms ◽  
Grey Scale ◽  
Fixed Set

Nowadays, satellite images are used in many applications, and their automatic processing is vital. Conventional integer grey-scale edge detection algorithms are often used for this. This study shows that the use of color-based, fractional order edge detection may enhance the results obtained using conventional techniques in satellite images. It also shows that it is possible to find a fixed set of parameters, allowing automatic detection while maintaining high performance.

scholarly journals Chaos in the discrete memristor-based system with fractional-order difference

2021 ◽  
Vol 24 ◽  
pp. 104106
Author(s):  
Yuexi Peng ◽  
Shaobo He ◽  
Kehui Sun
Keyword(s):  
Fractional Order ◽  
Order Difference

scholarly journals Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
Mary Jacintha ◽  
Abdullah Özbekler
Keyword(s):  
Fractional Order ◽  
Difference Equations ◽  
Difference Operator ◽  
Fractional Operators ◽  
Damping Term ◽  
Fractional Difference ◽  
Riccati Technique ◽  
Order Difference ◽  
Numerical Examples ◽  
Positive Integers

The paper studies the oscillation of a class of nonlinear fractional order difference equations with damping term of the form Δψλzηλ+pλzηλ+qλF∑s=λ0λ−1+μ λ−s−1−μys=0, where zλ=aλ+bλΔμyλ, Δμ stands for the fractional difference operator in Riemann-Liouville settings and of order μ, 0<μ≤1, and η≥1 is a quotient of odd positive integers and λ∈ℕλ0+1−μ. New oscillation results are established by the help of certain inequalities, features of fractional operators, and the generalized Riccati technique. We verify the theoretical outcomes by presenting two numerical examples.

scholarly journals Fractional-Order SIR Epidemic Model for Transmission Prediction of COVID-19 Disease

2020 ◽  
Vol 10 (23) ◽  
pp. 8316
Author(s):  
Kamil Kozioł ◽  
Rafał Stanisławski ◽  
Grzegorz Bialic
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Dynamic Properties ◽  
Sir Model ◽  
Domain Model ◽  
Sir Epidemic Model ◽  
Step Method ◽  
Order Difference ◽  
Sir Epidemic ◽  
The Time Domain

In this paper, the fractional-order generalization of the susceptible-infected-recovered (SIR) epidemic model for predicting the spread of the COVID-19 disease is presented. The time-domain model implementation is based on the fixed-step method using the nabla fractional-order difference defined by Grünwald-Letnikov formula. We study the influence of fractional order values on the dynamic properties of the proposed fractional-order SIR model. In modeling the COVID-19 transmission, the model’s parameters are estimated while using the genetic algorithm. The model prediction results for the spread of COVID-19 in Italy and Spain confirm the usefulness of the introduced methodology.

scholarly journals Linear isomorphic spaces of fractional-order difference operators

2021 ◽  
Vol 60 (1) ◽  
pp. 1155-1164 ◽  
Author(s):  
S.A. Mohiuddine ◽  
Kuldip Raj ◽  
M. Mursaleen ◽  
Abdullah Alotaibi
Keyword(s):  
Fractional Order ◽  
Difference Operators ◽  
Order Difference
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