The phase space for nonlinear hyperbolic functional differential equations with unbounded delay is constructed. The set of axioms for generalized solutions of initial problems is presented. A theorem on the existence and continuous dependence upon initial data is given. The Cauchy problem is transformed into a system of integral functional equations. The existence of solutions of this system is...

In this paper, we design an observer for a system represented by general class of Integral Delay Equations (IDE). This equations encompasses various systems, from chemical or biological processes to the propagation electric pulses on excitable media. The available measurement corresponds discrete and distributed-delayed value state. Under appropriate spectral observability assumption, implement...

Fractional differential equations are a very important tool in modelling many phenomena of physics and, therefore, they deserve an independent study of their theories parallel to the well-known theory of differential equations, [10, 12, 15, 17]. On the other hand, a great number of papers about differential and integral equations with a modified argument have appeared in the literature recently...

substantiation of the averaging method for differential equations with maxima is presented. two theorems on substantiates for differential equations with maxima are established.

The aim of this paper is to establish a connecting thread through the probabilistic concepts of pth-moment Lyapunov exponents, the integral averaging method, and Hale’s reduction approach for delay dynamical systems. We demonstrate this connection by studying the stability of perturbed deterministic and stochastic differential equations with fixed time delays in the displacement and derivative ...

In this work, we present a computational method for solving second kindnonlinear Fredholm Volterra integral equations which is based on the use ofHaar wavelets. These functions together with the collocation method are thenutilized to reduce the Fredholm Volterra integral equations to the solution ofalgebraic equations. Finally, we also give some numerical examples that showsvalidity and applica...

Degenerate kernel approximation method is generalized to solve Hammerstein system of Fredholm integral equations of the second kind. This method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. Convergence analysis is investigated and on some test problems, the propo...

on a time scale T, here (s) = |s|γ –2s, γ > 1 with a, p and q are positive real-valued rd-continuous functions defined on T. By using the Riccati transformation technique and integral averaging technique, some new sufficient conditions, which ensure that every solution oscillates, are established. Our results in this paper not only extend and improve the known results, but also unify the result...