Nonlinear Integrodifferential Equations with Time Varying Delay

Finite time stabilization of time-delay nonlinear systems with uncertainty and time-varying delay

In this paper, the problem of finite-time stability and finite-time stabilization for a specific class of dynamical systems with nonlinear functions in the presence time-varying delay and norm-bounded uncertainty terms is investigated. Nonlinear functions are considered to satisfy the Lipchitz conditions. At first, sufficient conditions to guarantee the finite-time stability for time-delay nonl...

Ulam stabilities for nonlinear Volterra-Fredholm delay integrodifferential equations

In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of ob...

Solvability of Nonautonomous Fractional Integrodifferential Equations with Infinite Delay

Zuomao Yan EXISTENCE OF SOLUTIONS FOR SOME NONLINEAR DELAY INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL INITIAL CONDITIONS

The main purpose of this paper is the existence of mild solutions for a class of first-order nonlinear delay integrodifferential equations with nonlocal initial conditions in Banach spaces. We show that the solutions are given by the application of the theory of resolvent operators and the Sadovskii’s fixed point theorem. An example is presented in the end to show the applications of the obtain...

Sliding Mode Control of Nonlinear Systems with Time-varying Delay

This paper considers a sliding mode control of multivariable nonlinear systems with time-varying delay. In our previous work, a sliding mode control design method combining with the finite spectrum assignment has been developed. In the design method, the sliding surface is constructed by using a coordinates transformation containing past values of the state variables. In most practical systems,...