Study on A Combined Optimal Rational Approximation Method of Fractional-order Calculus Operator and Its Application

2017 ◽  
Vol 10 (3) ◽  
Author(s):  
Huimin Zhao ◽  
Chen Guo ◽  
Wu Deng
Keyword(s):  
Fractional Order ◽  
Rational Approximation ◽  
Approximation Method ◽  
Fractional Order Calculus

Sub-Optimum H2 Rational Approximations to Fractional Order Linear Systems

2005 ◽  
Author(s):  
Dingyu¨ Xue ◽  
YangQuan Chen
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Rational Approximation ◽  
Approximation Method ◽  
Linear Time ◽  
Rational Approximations ◽  
Order Linear ◽  
Integer Order ◽  
Linear Time Invariant ◽  
Time Invariant

In this paper, we propose a procedure to achieve rational approximation to arbitrary fractional order linear time invariant (FO-LTI) systems with sub-optimum H2-norm. Through illustrations, we show that the rational approximation is simple and effective. It is also demonstrated that this sub-optimum approximation method is effective in designing integer order controllers for FO-LTI systems in general form. Useful Matlab codes are also given in the appendices.

Predicting the aggressiveness of peripheral zone prostate cancer using a fractional order calculus diffusion model

2021 ◽  
Vol 143 ◽  
pp. 109913
Author(s):  
Zhihua Li ◽  
Guangyu Dan ◽  
Vikram Tammana ◽  
Scott Johnson ◽  
Zheng Zhong ◽  
...  
Keyword(s):  
Prostate Cancer ◽  
Diffusion Model ◽  
Fractional Order ◽  
Peripheral Zone ◽  
Fractional Order Calculus

scholarly journals Studies of anomalous diffusion in the human brain using fractional order calculus

2010 ◽  
Vol 63 (3) ◽  
pp. 562-569 ◽  
Author(s):  
Xiaohong Joe Zhou ◽  
Qing Gao ◽  
Osama Abdullah ◽  
Richard L. Magin
Keyword(s):  
Human Brain ◽  
Fractional Order ◽  
Anomalous Diffusion ◽  
Fractional Order Calculus

scholarly journals Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Wang ◽  
Yuangui Zhou ◽  
Jianyi Xue ◽  
Delan Zhu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Wide Class ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Order System ◽  
Fractional Order Calculus ◽  
Simulation Results ◽  
The Stability

We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

Analysis of a Nonlinear System with a Random Parameter

2014 ◽  
Vol 721 ◽  
pp. 366-369
Author(s):  
Hong Gang Dang ◽  
Xiao Ya Yang ◽  
Wan Sheng He
Keyword(s):  
Nonlinear System ◽  
Fractional Order ◽  
Approximation Method ◽  
Lorenz System ◽  
Laguerre Polynomial ◽  
Random Parameter ◽  
Order System ◽  
Order Complex ◽  
Ensemble Mean ◽  
Complex Lorenz System

In this paper, a nonlinear system with random parameter, which is called stochastic fractional-order complex Lorenz system, is investigated. The Laguerre polynomial approximation method is used to study the system. Then, the stochastic fractional-order system is reduced into the equivalent deterministic one with Laguerre approximation. The ensemble mean and sample responses of the stochastic system can be obtained.

Formulation of Fractional Derivative-Based De-Hazing Algorithm and Implementation on Mobile-Embedded Devices

2019 ◽  
Vol 19 (01) ◽  
pp. 1950003
Author(s):  
Uche A. Nnolim
Keyword(s):  
Image Processing ◽  
Fractional Derivative ◽  
Mobile Devices ◽  
Fractional Order ◽  
Spatial Filter ◽  
Embedded Devices ◽  
Processing Application ◽  
Fractional Order Calculus ◽  
Image Processing Application ◽  
Logarithmic Image Processing

This paper presents the modification of a previously developed algorithm using fractional order calculus and its implementation on mobile-embedded devices such as smartphones. The system performs enhancement on three categories of images such as those exhibiting uneven illumination, faded features/colors and hazy appearance. The key contributions include the simplified scheme for illumination correction, contrast enhancement and de-hazing using fractional derivative-based spatial filter kernels. These are achieved without resorting to logarithmic image processing, histogram-based statistics and complex de-hazing techniques employed by conventional algorithms. The simplified structure enables ease of implementation of the algorithm on mobile devices as an image processing application. Results indicate that the fractional order version of the algorithm yields good results relative to the integer order version and other algorithms from the literature.

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