In this work, we study the oscillation of fourth order neutral differential equations with delay argument. By means generalized Riccati transformation technique, obtain new criteria for equation. An example is given to clarify main results in paper.

Using the idea of the very recently generalized Kudryashov method and based on a generalized Riccati equation we present an alternative method which can be considered as an extension of the well known tanh method. As application of the proposed method, we obtain exact solutions of the Dispersive modified Benjamin-Bona-Mahony equation showing in this way its effectiveness. Mathematics Subject Cl...

We introduce a transformation between the discrete-time and continuoustime algebraic Riccati equations. We show that under mild conditions the two algebraic Riccati equations can be transformed from one to another, and both algebraic Riccati equations share common Hermitian solutions. The transformation also sets up the relations about the properties, commonly in system and control setting, tha...

We consider a stochastic linear–quadratic (LQ) problem with possible indefinite cost weighting matrices for the state and the control. An outstanding open problem is to identify an appropriate Riccati-type equation whose solvability is equivalent to the solvability of this possibly indefinite LQ problem. In this paper we introduce a new type of differential Riccati equation, called the generali...

in the present work, a hybrid of fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. the fourier transform is employed with combination of homotopy perturbation method (hpm), the so called fourier transform homotopy perturbation method (fthpm) to solve the partial differential equations. the c...

a mathematical model is presented in the present study to control‎ ‎the light propagation in an inhomogeneous media‎. ‎the method is ‎based on the identification of the optimal materials distribution‎ ‎in the media such that the trajectories of light rays follow the‎ ‎desired path‎. ‎the problem is formulated as a distributed parameter ‎identification problem and it is solved by a numerical met...

The paper deals with the associated algebraic matrix Riccati equation (AAMRE), closely related to the standard algebraic matrix Riccati equation arising in the theory of linear-quadratic optimisation and filtering. The sensitivity of the AAMRE relative to perturbations in its coefficients is studied. Both linear local (norm-wise and componentwise) and non-linear non-local perturbation bounds ar...

Let R be a commutative complex unital semisimple Banach algebra with the involution ·⋆. Sufficient conditions are given for the existence of a stabilizing solution to the H ∞ Riccati equation when the matricial data has entries from R. Applications to spatially distributed systems are discussed.