scholarly journals Video-based fractional order identification of diffusion dynamics for the analysis of migration rates of polar and nonpolar liquids: Water and oil studies

2021 ◽  
Vol 92 (3) ◽  
pp. 035106
Author(s):  
Stefani I. E. Andrade ◽  
Roberto K. H. Galvão ◽  
Mario C. U. Araujo ◽  
Sillas Hadjiloucas
Keyword(s):  
Fractional Order ◽  
Migration Rates ◽  
Diffusion Dynamics ◽  
Nonpolar Liquids

Controlling Bifurcations in Fractional-Delay Systems with Colored Noise

2018 ◽  
Vol 28 (11) ◽  
pp. 1850137 ◽  
Author(s):  
Jintian Zhang ◽  
Zhongkui Sun ◽  
Xiaoli Yang ◽  
Wei Xu
Keyword(s):  
Fractional Order ◽  
Bifurcation Point ◽  
Colored Noise ◽  
Delay System ◽  
Delayed Feedback ◽  
Delay Systems ◽  
Stochastic Bifurcation ◽  
Fractional Order Systems ◽  
Diffusion Dynamics ◽  
Fractional Delay

Comparing with the traditional integer-order model, fractional-order systems have shown enormous advantages in the analysis of new materials and anomalous diffusion dynamics mechanism in the past decades, but the research has been confined to fractional-order systems without delay. In this paper, we study the fractional-delay system in the presence of both the colored noise and delayed feedback. The stationary density functions (PDFs) are derived analytically by means of the stochastic averaging method combined with the principle of minimum mean-square error, by which the stochastic bifurcation behaviors have been well identified and studied. It can be found that the fractional-orders have influences on the bifurcation behaviors of the fractional-order system, but the bifurcation point of stationary PDF for amplitude differs from the bifurcation point of joint PDF. By merely changing the colored noise intensity or correlation time the shape of the PDFs can switch between unimodal distribution and bimodal one, thus announcing the occurrence of stochastic bifurcation. Further, we have demonstrated that modulating the time delay or delayed feedback may control bifurcation behaviors. The perfect agreement between the theoretical solution and the numerical solution obtained by the predictor–corrector algorithm confirms the correctness of the conclusion. In addition, fractional-order dominates the bifurcation control in the fractional-delay system, which causes the sensitive dependence of other bifurcation parameters on fractional-order.

Stability in a Discrete Fractional Order Prey Predator System with Functional Response

2017 ◽  
Vol 7 (5) ◽  
pp. 630-633 ◽  
Author(s):  
A. George Maria Selvam ◽  
◽  
R. Janagaraj ◽  
Britto Jacob. S ◽  
◽  
...  
Keyword(s):  
Functional Response ◽  
Fractional Order ◽  
Predator System

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

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