scholarly journals Multiplicity result to a system of over-determined Fredholm fractional integro-differential equations on time scales

2021 ◽  
Vol 7 (2) ◽  
pp. 2646-2665
Author(s):  
Xing Hu ◽  
◽  
Yongkun Li
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Time Scales ◽  
Multiplicity Result

<abstract><p>In present paper, several conditions ensuring existence of three distinct solutions of a system of over-determined Fredholm fractional integro-differential equations on time scales are derived. Variational methods are utilized in the proofs.</p></abstract>

scholarly journals Li–Yorke Chaos in Hybrid Systems on a Time Scale

2015 ◽  
Vol 25 (14) ◽  
pp. 1540024 ◽  
Author(s):  
Marat Akhmet ◽  
Mehmet Onur Fen
Keyword(s):  
Differential Equations ◽  
Hybrid Systems ◽  
Time Scales ◽  
Time Scale ◽  
Impulsive Differential Equations ◽  
Reduction Technique ◽  
Duffing Equation ◽  
Dynamic Equations ◽  
Definition Of ◽  
First Time

By using the reduction technique to impulsive differential equations [Akhmet & Turan, 2006], we rigorously prove the presence of chaos in dynamic equations on time scales (DETS). The results of the present study are based on the Li–Yorke definition of chaos. This is the first time in the literature that chaos is obtained for DETS. An illustrative example is presented by means of a Duffing equation on a time scale.

Lyapunov stability for measure differential equations and dynamic equations on time scales

2019 ◽  
Vol 267 (7) ◽  
pp. 4192-4223 ◽  
Author(s):  
M. Federson ◽  
R. Grau ◽  
J.G. Mesquita ◽  
E. Toon
Keyword(s):  
Differential Equations ◽  
Time Scales ◽  
Lyapunov Stability ◽  
Dynamic Equations

On the Equivalence of Normal Form Theory and Multiple Time Scale Method

2007 ◽  
Author(s):  
Fengxia Wang ◽  
Anil K. Bajaj
Keyword(s):  
Nonlinear Systems ◽  
Normal Form ◽  
Differential Equations ◽  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Perturbation Scheme ◽  
Normal Form Theory ◽  
Weakly Nonlinear ◽  
Form Theory

Multiple time scales technique has long been an important method for the analysis of weakly nonlinear systems. In this technique, a set of multiple time scales are introduced that serve as the independent variables. The evolution of state variables at slower time scales is then determined so as to make the expansions for solutions in a perturbation scheme uniform in natural and slower times. Normal form theory has also recently been used to approximate the dynamics of weakly nonlinear systems. This theory provides a way of finding a coordinate system in which the dynamical system takes the “simplest” form. This is achieved by constructing a series of near-identity nonlinear transformations that make the nonlinear systems as simple as possible. The “simplest” differential equations obtained by the normal form theory are topologically equivalent to the original systems. Both methods can be interpreted as nonlinear perturbations of linear differential equations. In this work, the equivalence of these two methods for constructing periodic solutions is proven, and it is explained why some studies have found the results obtained by the two techniques to be inconsistent.

Sign in / Sign up

Export Citation Format

Share Document