BLOW-UP PHENOMENA PROFILE FOR HADAMARD FRACTIONAL DIFFERENTIAL SYSTEMS IN FINITE TIME

Fractals ◽  
2019 ◽  
Vol 27 (06) ◽  
pp. 1950093 ◽  
Author(s):  
LI MA
Keyword(s):  
Banach Space ◽  
Lipschitz Condition ◽  
General Condition ◽  
Finite Time ◽  
Blow Up ◽  
Differential Systems ◽  
Functional Operator ◽  
Fractional Differential Systems ◽  
Fractional Differential ◽  
Theoretical Results

The main purpose of this paper is to investigate the weak singularity of solutions for some nonlinear Hadamard fractional differential systems (HFDSs). By constructing proper Banach space and employing lower and upper solutions technique, we prove the existence of the blow-up solutions for a class of HFDSs. In addition, we establish a more general condition than the classical Lipschitz condition which is employed to guarantee the equivalence between the solutions to HFDS and the corresponding functional operator. Also several examples are presented to verify our theoretical results.

On the kinetics of Hadamard-type fractional differential systems

2020 ◽  
Vol 23 (2) ◽  
pp. 553-570 ◽  
Author(s):  
Li Ma
Keyword(s):  
Differential Operator ◽  
Numerical Simulations ◽  
Type Inequality ◽  
The Other ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Kinetics Of ◽  
Theoretical Results

AbstractThis paper is devoted to the investigation of the kinetics of Hadamard-type fractional differential systems (HTFDSs) in two aspects. On one hand, the nonexistence of non-trivial periodic solutions for general HTFDSs, which are considered in some functional spaces, is proved and the corresponding eigenfunction of Hadamard-type fractional differential operator is also discussed. On the other hand, by the generalized Gronwall-type inequality, we estimate the bound of the Lyapunov exponents for HTFDSs. In addition, numerical simulations are addressed to verify the obtained theoretical results.

scholarly journals Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 107
Author(s):  
Daliang Zhao ◽  
Juan Mao
Keyword(s):  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Integral Boundary ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Existence And Multiplicity ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann–Stieltjes coupled integral boundary value conditions in Banach Spaces. Nonlinear functions f(t,u,v) and g(t,u,v) in the considered systems are allowed to be singular at every variable. The boundary conditions here are coupled forms with Riemann–Stieltjes integrals. In order to overcome the difficulties arising from the singularity, a suitable cone is constructed through the properties of Green’s functions associated with the systems. The main tool used in the present paper is the fixed point theorem on cone. Lastly, an example is offered to show the effectiveness of our obtained new results.

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.

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