Lim, S. C.; Li, Ming; Teo, L. P. Langevin equation with two fractional orders. (English) Zbl 1225.82049 Phys. Lett., A 372, No. 42, 6309-6320 (2008). Summary: A new type of fractional Langevin equation of two different orders is introduced. The solutions for this equation, known as the fractional Ornstein-Uhlenbeck processes, based on Weyl and Riemann-Liouville fractional derivatives are obtained. The basic properties of these processes are studied. An example of the spectral density of ocean wind speed which has similar spectral density as that of Weyl fractional Ornstein-Uhlenbeck process is given. Cited in 74 Documents MSC: 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics 28A80 Fractals 26A33 Fractional derivatives and integrals 34K37 Functional-differential equations with fractional derivatives Keywords:fractional Langevin equation; Weyl and Riemann-Liouville fractional derivatives; short range dependence; fractal dimension PDF BibTeX XML Cite \textit{S. C. Lim} et al., Phys. Lett., A 372, No. 42, 6309--6320 (2008; Zbl 1225.82049) Full Text: DOI OpenURL References: [1] () [2] Mazo, R., Brownian motion: fluctuations, dynamics and applications, (2002), Oxford Univ. Press Oxford · Zbl 1140.60001 [3] Coffey, W.T.; Kalmykov, Yu.P.; Waldron, J.T., The Langevin equation, (2004), World Scientific Singapore · Zbl 0952.82510 [4] Wang, K.G., Phys. rev. A, 45, 833, (1992) [5] Porra, J.M.; Wang, K.G.; Masoliver, J., Phys. rev. 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