Normal Form of Bifurcation for Caputo-Hadamard Fractional Differential System With a Parameter

2021 ◽  
Author(s):  
Chuntao Yin
Keyword(s):  
Normal Form ◽  
Differential System ◽  
Implicit Function Theorem ◽  
Pitchfork Bifurcation ◽  
Implicit Function ◽  
Fractional Differential System ◽  
Fractional Differential

Abstract This paper focuses on the normal form computation of the pitchfork bifurcation for the Caputo-Hadamard fractional differential system with a parameter. By using Taylor’s expansion and Implicit Function Theorem, we derive the normal form of the pitchfork bifurcation for the Caputo-Hadamard fractional differential system with a parameter.

GENERATING 3-D SCROLL GRID ATTRACTORS OF FRACTIONAL DIFFERENTIAL SYSTEMS VIA STAIR FUNCTION

2007 ◽  
Vol 17 (11) ◽  
pp. 3965-3983 ◽  
Author(s):  
WEIHUA DENG
Keyword(s):  
Differential System ◽  
Autonomous System ◽  
Function Approach ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential System ◽  
Linear Autonomous System ◽  
Fractional Differential ◽  
The One ◽  
Number Of Equilibria

This paper discusses the stair function approach for the generation of scroll grid attractors of fractional differential systems. The one-directional (1-D) n-grid scroll, two-directional (2-D) (n × m)-grid scroll and three-directional (3-D) (n × m × l)-grid scroll attractors are created from a fractional linear autonomous system with a simple stair function controller. Being similar to the scroll grid attractors of classical differential systems, the scrolls of 1-D n-grid scroll, 2-D (n × m)-grid scroll and 3-D (n × m × l)-grid scroll attractors are located around the equilibria of fractional differential system on a line, on a plane or in 3D, respectively and the number of scrolls is equal to the corresponding number of equilibria.

scholarly journals Stability results for the linear degenerate fractional differential system

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Zhixin Zhang ◽  
Jia-Bao Liu ◽  
Jinde Cao ◽  
Wei Jiang ◽  
Ahmed Alsaedi ◽  
...  
Keyword(s):  
Differential System ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
Stability Results ◽  
Linear Degenerate

scholarly journals Nontrivial Solution of Fractional Differential System Involving Riemann-Stieltjes Integral Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Ge-Feng Yang
Keyword(s):  
Nontrivial Solution ◽  
Differential System ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Integral Condition ◽  
Contraction Mapping Principle ◽  
Stieltjes Integral ◽  
Fractional Differential System ◽  
Nonlinear Alternative ◽  
Fractional Differential

We study the existence and uniqueness of nontrivial solutions for a class of fractional differential system involving the Riemann-Stieltjes integral condition, by using the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle, some sufficient conditions of the existence and uniqueness of a nontrivial solution of a system are obtained.

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