scholarly journals Qualitative Analysis of some Types of Neutral Delay Differential Equations

2021 ◽  
pp. 3634-3641
Author(s):  
May Mohammed Helal
Keyword(s):  
Qualitative Analysis ◽  
Contraction Mapping ◽  
Necessary Conditions ◽  
Zero Solution ◽  
Neutral Delay ◽  
Contraction Mapping Theorem ◽  
Banach Contraction ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
Banach Contraction Mapping

     In this paper, we conduct some qualitative analysis that involves the global asymptotic stability (GAS) of the Neutral Differential Equation (NDE) with variable delay, by using  Banach contraction mapping theorem, to give some necessary conditions to achieve the GAS of the zero solution.

scholarly journals Boundary controllability of nonlinear stochastic fractional systems in Hilbert spaces

2018 ◽  
Vol 28 (1) ◽  
pp. 123-133 ◽  
Author(s):  
Rajendran Mabel Lizzy ◽  
Krishnan Balachandran
Keyword(s):  
Hilbert Spaces ◽  
Contraction Mapping ◽  
Control Function ◽  
Sufficient Conditions ◽  
Contraction Mapping Theorem ◽  
Boundary Controllability ◽  
Fractional Systems ◽  
Banach Contraction ◽  
Linear And Nonlinear Systems ◽  
Banach Contraction Mapping

AbstractSufficient conditions for the controllability of nonlinear stochastic fractional boundary control systems are established. The equivalent integral equations are derived for both linear and nonlinear systems, and the control function is given in terms of the pseudoinverse operator. The Banach contraction mapping theorem is used to obtain the result. A controllability result for nonlinear stochastic fractional integrodifferential systems is also attained. Examples are included to illustrate the theory.

scholarly journals Stability and Square Integrability of Solutions to third order Neutral Delay Differential Equations

2018 ◽  
Vol 71 (1) ◽  
pp. 81-97 ◽  
Author(s):  
John R. Graef ◽  
Linda D. Oudjedi ◽  
Moussadek Remili
Keyword(s):  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Neutral Delay ◽  
Third Order ◽  
Neutral Delay Differential Equation ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Square Integrability ◽  
Delay Differential

Abstract In this paper, sufficient conditions to guarantee the square integrability of all solutions and the asymptotic stability of the zero solution of a non-autonomous third-order neutral delay differential equation are established. An example is given to illustrate the main results.

scholarly journals Some Further Results on Oscillations for Neutral Delay Differential Equations with Variable Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Variable Coefficients ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
Neutral Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

We study the oscillatory behaviour of all solutions of first-order neutral equations with variable coefficients. The obtained results extend and improve some of the well-known results in the literature. Some examples are given to show the evidence of our new results.

scholarly journals Oscillation and Asymptotic Properties of Differential Equations of Third-Order

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 192
Author(s):  
R. Elayaraja ◽  
V. Ganesan ◽  
Omar Bazighifan ◽  
Clemente Cesarano
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Neutral Delay ◽  
Third Order ◽  
Riccati Technique ◽  
Neutral Delay Differential Equations ◽  
The Subject ◽  
Delay Differential ◽  
New Criteria ◽  
Noncanonical Operator

The main purpose of this study is aimed at developing new criteria of the iterative nature to test the asymptotic and oscillation of nonlinear neutral delay differential equations of third order with noncanonical operator (a(ι)[(b(ι)x(ι)+p(ι)x(ι−τ)′)′]β)′+∫cdq(ι,μ)xβ(σ(ι,μ))dμ=0, where ι≥ι0 and w(ι):=x(ι)+p(ι)x(ι−τ). New oscillation results are established by using the generalized Riccati technique under the assumption of ∫ι0ιa−1/β(s)ds<∫ι0ι1b(s)ds=∞asι→∞. Our new results complement the related contributions to the subject. An example is given to prove the significance of new theorem.

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