A generalized Chebyshev wavelet operational matrix (CWOM) is presented for the solution of nonlinear Riccati differential equations. The operational matrix together with suitable collocation points converts the fractional order Riccati differential equations into a system of algebraic equations. Accuracy and efficiency of the proposed method is verified through numerical examples and comparison...

I perform the factorization(s) of the Wheeler-DeWitt equation for the FRW minisuperspace universes of arbitrary Hartle-Hawking factor ordering introducing by this means a new, Darboux-type, free parameter in “quantum” cosmology. This parameter can be thought of as giving the time scale of a force due to a cosmological field. Mathematically speaking, the parameter is a Riccati integration consta...

In this paper, by using the generalized Riccati technique and the integral averaging technique, some new oscillation criteria for certain second order retarded differential equation of the form

We consider a nonlinear partial differential equation for complexvalued functions which is related to the two-dimensional stationary Schrödinger equation and enjoys many properties similar to those of the ordinary differential Riccati equation as, e.g., the famous Euler theorems, the Picard theorem and others. Besides these generalizations of the classical “one-dimensional” results we discuss n...

We first obtain by analogy with the continuous (differential) case the general solution of the discrete Riccati equation. Moreover, we establish the full equivalence between our discrete Riccati equation and a corresponding homogeneous second order discrete linear equation. Our results can be considered the discrete analog of Mielnik's construction in supersymmetric quantum mechanics [J. Math. ...

In this paper we present a Nash equilibrium problem of linear quadratic zero-sum dynamic games for descriptor system. We assume that the players give a linear feedback to the game. For the game with finite planning horizon we derive a differential Riccati type equation. For the game with infinite planning horizon we consider an algebraic Riccati type equation. The connection of the game solutio...