Integral inequalities and exponential convergence of solutions of differential equations with bounded delay

1982 ◽  
pp. 56-68
Author(s):  
F. V. Atkinson ◽  
J. R. Haddock ◽  
O. J. Staffans
Keyword(s):  
Differential Equations ◽  
Exponential Convergence ◽  
Integral Inequalities ◽  
Bounded Delay ◽  
Convergence Of Solutions

scholarly journals Exponential Decay for a System of Equations with Distributed Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Nasser-Eddine Tatar
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Exponential Decay ◽  
Distributed Delay ◽  
Distributed Delays ◽  
System Of Equations ◽  
Activation Functions ◽  
Convergence Of Solutions

We prove convergence of solutions to zero in an exponential manner for a system of ordinary differential equations. The feature of this work is that it deals with nonlinear non-Lipschitz and unbounded distributed delay terms involving non-Lipschitz and unbounded activation functions.

scholarly journals The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities

2019 ◽  
Vol 52 (1) ◽  
pp. 204-212 ◽  
Author(s):  
Fuat Usta ◽  
Mehmet Zeki Sarıkaya
Keyword(s):  
Differential Equations ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Integral Inequalities ◽  
Fractional Operator ◽  
Van Der Pol ◽  
Global Existence Of Solutions ◽  
Explicit Bounds ◽  
Fractional Differential ◽  
Conformable Fractional Integral

AbstractIn this study we introduced and tested retarded conformable fractional integral inequalities utilizing non-integer order derivatives and integrals. In line with this purpose, we used the Katugampola type conformable fractional calculus which has several practical properties. These inequalities generalize some famous integral inequalities which provide explicit bounds on unknown functions. The results provided here had been implemented to the global existence of solutions to the conformable fractional differential equations with time delay.

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