scholarly journals Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zhi-Yong Chen ◽  
Carlo Cattani ◽  
Wei-Ping Zhong
Keyword(s):  
Signal Processing ◽  
Fourier Series ◽  
Fractional Calculus ◽  
Present Method ◽  
Continuous Functions ◽  
Cantor Sets ◽  
Point Of View ◽  
Local Fractional Calculus ◽  
Processing Point

From the signal processing point of view, the nondifferentiable data defined on the Cantor sets are investigated in this paper. The local fractional Fourier series is used to process the signals, which are the local fractional continuous functions. Our results can be observed as significant extensions of the previously known results for the Fourier series in the framework of the local fractional calculus. Some examples are given to illustrate the efficiency and implementation of the present method.

scholarly journals Mathematical Models Arising in the Fractal Forest Gap via Local Fractional Calculus

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Chun-Ying Long ◽  
Yang Zhao ◽  
Hossein Jafari
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Mathematical Models ◽  
Cantor Sets ◽  
Forest Gap ◽  
Local Fractional Derivative ◽  
Local Fractional Calculus ◽  
Growth Equations ◽  
Gap Models ◽  
Individual Trees

The forest new gap models via local fractional calculus are investigated. The JABOWA and FORSKA models are extended to deal with the growth of individual trees defined on Cantor sets. The local fractional growth equations with local fractional derivative and difference are discussed. Our results are first attempted to show the key roles for the nondifferentiable growth of individual trees.

A SIMILARITY METRIC IN IMAGE SEARCHING

2007 ◽  
Vol 07 (02) ◽  
pp. 211-225
Author(s):  
XUELONG LI ◽  
JING LI ◽  
DACHENG TAO ◽  
YUAN YUAN
Keyword(s):  
Signal Processing ◽  
System Performance ◽  
Ground Truth ◽  
Point Of View ◽  
Visual Features ◽  
Similarity Metrics ◽  
Graphical Interface ◽  
Similarity Metric ◽  
Processing Point ◽  
Small Image

Similarity metric is a key component in query-by-example image searching with visual features. After extraction of image visual features, the scheme of computing their similarities can affect the system performance dramatically — the image searching results are normally displayed in decreasing order of similarity (alternatively, increasing order of distance) on the graphical interface for end users. Unfortunately, conventional similarity metrics, in image searching with visual features, usually encounter several difficulties, namely, lighting, background, and viewpoint problems. From the signal processing point of view, this paper introduces a novel similarity metric and therefore reduces the above three problems to some extent. The effectiveness of this newly developed similarity metric is demonstrated by a set of experiments upon a small image ground truth.

scholarly journals Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
H. M. Srivastava ◽  
Alireza Khalili Golmankhaneh ◽  
Dumitru Baleanu ◽  
Xiao-Jun Yang
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Analytical Solutions ◽  
Initial Value Problems ◽  
Fractional Derivatives ◽  
Cantor Sets ◽  
Coupling Method ◽  
Initial Value ◽  
Local Fractional Calculus ◽  
Sumudu Transform

Local fractional derivatives were investigated intensively during the last few years. The coupling method of Sumudu transform and local fractional calculus (called as the local fractional Sumudu transform) was suggested in this paper. The presented method is applied to find the nondifferentiable analytical solutions for initial value problems with local fractional derivative. The obtained results are given to show the advantages.

scholarly journals New Approaches for Solving Fokker Planck Equation on Cantor Sets within Local Fractional Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Hassan Kamil Jassim
Keyword(s):  
Fractional Calculus ◽  
Planck Equation ◽  
Cantor Sets ◽  
Fractional Operators ◽  
New Approaches ◽  
Fokker Planck Equation ◽  
Local Fractional Calculus ◽  
Iteration Methods ◽  
Fractional Differential ◽  
Fokker Planck

We discuss new approaches to handling Fokker Planck equation on Cantor sets within local fractional operators by using the local fractional Laplace decomposition and Laplace variational iteration methods based on the local fractional calculus. The new approaches maintain the efficiency and accuracy of the analytical methods for solving local fractional differential equations. Illustrative examples are given to show the accuracy and reliable results.

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