some preliminaries about the integrable families of riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional schrodinger equation with the kerr law nonlinearity. finally by using of this method and solutions of ri...

In this paper we consider a class of matrix Riccati equations arising from stochastic LQR problems. We prove a monotonicity of solutions to the differential Riccati equations, which leads to a necessary and sufficient condition for the existence of solutions to the algebraic Riccati equations. In addition, we obtain results on comparison, uniqueness, stabilizability and approximation for soluti...

In this paper we consider a class of matrix Riccati equations arising from stochastic LQR problems. We prove a monotonicity of solutions to the differential Riccati equations, which leads to a necessary and sufficient condition for the existence of solutions to the algebraic Riccati equations. In addition, we obtain results on comparison, uniqueness, stabilizability and approximation for soluti...

Some preliminaries about the integrable families of Riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional Schrodinger equation with the kerr law nonlinearity. Finally by using of this method and solutions of Ri...

This is a continuation of the paper [12]. We consider general matrix Riccati equations, including those from stochastic linear regulator problems with infinite horizon. For differential Riccati equations, we prove a monotonicity of solutions, which leads to a necessary and sufficient condition for the existence of solutions to algebraic Riccati equations. For solutions to the algebraic Riccati ...

We survey recent and also older results on nonsymmetric matrix Riccati differential equations and in the time invariant case on the corresponding algebraic Riccati equations. In particular we cite various applications connected with matrix Riccati equations.

This paper is concerned with rational matrix equations occuring in stochastic control that play an analogous role as the algebraic Riccati equation does in deterministic control. We will therefore sometimes refer to these equations as stochastic (algebraic) Riccati equations. A first rigorous treatment of a stochastic Riccati equation from LQ-control theory seems to have been undertaken by Wonh...

In this paper, an iterative technique is proposed to solve linear integrated active/passive design problems. The optimality of active and passive parts leads to the nonlinear algebraic Riccati equation due to the active parameters and some associated additional Lyapunov equations due to the passive parameters. Rather than the solution of the nonlinear algebraic Riccati equation, it is proposed ...