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THE MATRIX RICCATI DIFFERENTIAL EQUATION AND THE SEMI-GROUP OF LINEAR FRACTIONAL TRANSFORMATIONS

Russian Mathematical Surveys, 1973
The matrix Riccati differential equation is discussed, from the point of view of dissipativity or conservativity of its solutions. A survey is given of results relating to analytic properties of these solutions and to the geometry of the corresponding semigroup of matrix linear fractional transformations; further, a probabilistic interpretation is ...
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Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations

Physics Letters A, 2012
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Numerical solutions of fractional Riccati type differential equations by means of the Bernstein polynomials

Applied Mathematics and Computation, 2013
The author constructs an approximate method to solve the Riccati fractional differential equation \[ \sum_{k=0}^{m}P_{k}(t)\frac{d^{k\alpha}y(t)}{dt^{k\alpha}}=A(t)+B(t)+C(t)y^{2} \] on \([0,R ...
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Lie symmetry analysis and solutions for a fractional Riccati–Bernoulli equation

International Journal of Dynamics and Control
Shaoru Liu, Yanxia Hu
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