Transform of Riccati equation of constant coefficients through fractional procedure

doi:10.1088/0305-4470/36/4/316

Transform of Riccati equation of constant coefficients through fractional procedure

H C Rosu et al 2003 J. Phys. A: Math. Gen. 36 1087-1093 doi: 10.1088/0305-4470/36/4/316

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H C Rosu¹, A L Madueño² and J Socorro²
¹ Department of Applied Mathematics, IPICyT, Apdo Postal 3-74 Tangamanga, San Luis Potosí, Mexico
² Instituto de Física, Universidad de Guanajuato, Apdo Postal E-143, León, Mexico
E-mail: hcr@ipicyt.edu.mx

Abstract. 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.

PACS numbers: 02.30.Hq, 04.20.Jb

Print publication: Issue 4 (31 January 2003)
Received 16 October 2002
Published 15 January 2003

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Transform of Riccati equation of constant coefficients through fractional procedure

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