Higher-Order Derivatives of Lyapunov Functions And Ultimate Boundedness in the Sense of Poisson of Solutions to Systems of Differential Equations

2018 ◽  
Vol 59 (6) ◽  
pp. 1100-1104 ◽  
Author(s):  
K. S. Lapin
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Higher Order ◽  
Ultimate Boundedness ◽  
Systems Of Differential Equations ◽  
Derivatives Of

scholarly journals Cone valued Lyapunov functions and Lipschitz stability of nonlinear systems of differential equations

1996 ◽  
Vol 19 (3) ◽  
pp. 435-440
Author(s):  
Olusola Akinyele
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Lyapunov Functions ◽  
Practical Stability ◽  
Lipschitz Stability ◽  
Comparison Result ◽  
Systems Of Differential Equations ◽  
New Concepts ◽  
Perturbed Systems

We introduce a new comparison result which will be an important tool when we apply cone valued Lyapunov like functions. We also introduce new concepts ofϕ0-uniform Lipschitz stability and(λ,λ,ϕ0)-practical stability and employ our comparison result to carry out stability analysis of nonlinear systems. Our results are also applicable to nonlinear perturbed systems.

scholarly journals Analytical Solutions of Fuzzy Linear Differential Equations in the Conformable Setting

2021 ◽  
Vol 2 (2) ◽  
pp. 13-30
Author(s):  
Awais Younus ◽  
Muhammad Asif ◽  
Usama Atta ◽  
Tehmina Bashir ◽  
Thabet Abdeljawad
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Analytical Solutions ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Conformable Derivative ◽  
Systems Of Differential Equations ◽  
Two Systems ◽  
Linear Differential

In this paper, we provide the generalization of two predefined concepts under the name fuzzy conformable differential equations. We solve the fuzzy conformable ordinary differential equations under the strongly generalized conformable derivative. For the order $\Psi$, we use two methods. The first technique is to resolve a fuzzy conformable differential equation into two systems of differential equations according to the two types of derivatives. The second method solves fuzzy conformable differential equations of order $\Psi$ by a variation of the constant formula. Moreover, we generalize our results to solve fuzzy conformable ordinary differential equations of a higher order. Further, we provide some examples in each section for the sake of demonstration of our results.

scholarly journals Some Properties of the Hermite Polynomials and Their Squares and Generating Functions

2016 ◽  
Author(s):  
Feng Qi ◽  
Bai-Ni Guo
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Hermite Polynomials ◽  
Higher Order ◽  
Explicit Formulas ◽  
Derivatives Of

In the paper, the authors consider the generating functions of the Hermite polynomials and their squares, present explicit formulas for higher order derivatives of the generating functions of the Hermite polynomials and their squares, which can be viewed as ordinary differential equations or derivative polynomials, find differential equations that the generating functions of the Hermite polynomials and their squares satisfy, and derive explicit formulas and recurrence relations for the Hermite polynomials and their squares.

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