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

In this paper, optimal control for stochastic linear quadratic singular neuro Takagi–Sugeno (T-S) fuzzy system with singular cost is obtained using genetic programming(GP). To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is computed by solving differential algebraic equation (DAE) using a novel and nontraditional GP approach. The obtained solution in t...

An error occurs in a part of the statement and proof Proposition 2.2 paper “Stochastic explosion non-uniqueness for α-Riccati equation” [J. Math. Anal. Appl. 476 (2019) 53–85] that is corrected this erratum. The revised result reveals new unexpected critical phenomena, having further implications solutions to nonlinear differential equation Riccati type.

In this paper, we applied a new analytical geometrical method which so called fractal index method to find a new solution of the generalized fractional Riccati equation of arbitrary order, we also wrote the solution on the closed form as an infinte series and showed that the series is convergent within some closed disk. The fractional operators are taken in sense of the Riemann-Liouville operat...