Exponential Stability of Nonlinear Time-Varying Delay Differential Equations via Lyapunov–Razumikhin Technique

Exponential stability of nonlinear time - varying differential equations and applications ∗

In this paper, we give sufficient conditions for the exponential stability of a class of nonlinear time-varying differential equations. We use the Lyapunov method with functions that are not necessarily differentiable; hence we extend previous results. We also provide an application to exponential stability for nonlinear time-varying control systems.

Inequalities and exponential decay in time varying delay differential equations

We use Lyapunov functionals to obtain sufficient conditions that guarantee exponential decay of solutions to zero of the time varying delay differential equation x ′ (t) = b(t)x(t) − a(t)x(t − h(t)). The highlights of the paper are allowing b(t) to change signs and the delay to vary with time. In addition, we obtain a criterion for the instability of the zero solution. Moreover, by comparison t...

Exponential Stability of Impulsive Delay Differential Equations

and Applied Analysis 3 Note that V(t∗) = Q(t∗) + C 2 ‖Φ‖ τ e ∫ t ∗

On exponential stability of nonlinear differential systems with time-varying delay

Solving nonlinear space-time fractional differential equations via ansatz method

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...