Transform of Riccati equation of constant coefficients through fractional procedure

Details Transform of Riccati equation of constant coefficients through fractional procedure Transform of Riccati equation of constant coefficients through fractional procedure

2001-12-12

arxiv.org/abs/math-ph/0112020v5

J. Phys. A 36 (2003) 1087-1094

Physics

Mathematical Physics

7 pages, 2 figures

Scientific paper

10.1088/0305-4470/36/4/316

We use a particular fractional generalization of the ordinary differential equations that we apply to the Riccati equation of constant coefficients. By this means the latter is transformed into a modified Riccati equation with the free term expressed as a power of the independent variable which is of the same order as the order of the applied fractional derivative. We provide the solutions of the modified equation and employ the results for the case of the cosmological Riccati equation of FRW barotropic cosmologies that has been recently introduced by Faraoni

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