Metzler, R.; Glöckle, W. G.; Nonnenmacher, T. F.; West, B. J. “Fractional tuning” of the Riccati equation. (English) Zbl 0913.34011 Fractals 5, No. 4, 597-601 (1997). The authors use fractal calculus (employing derivatives of fractional order) to study generalizations of the Riccati equation. They apply the procedure in the modelling of a freely falling body in a polymer fluid. Unlike the free-fall problem in the atmosphere (with air resistance) there is no terminal velocity in the polymer fluid.The paper is very well written. This reviewer found it to be quite engaging. It should be of interest and use to a wide range of analysts and theoreticians. the applications with differential equations beyond the Riccati equation seem yet to be developed. Reviewer: R.L.Huston (Cincinnati) Cited in 3 Documents MSC: 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 34A34 Nonlinear ordinary differential equations and systems 92E20 Classical flows, reactions, etc. in chemistry Keywords:nonlinear differential equations; Riccati equations; fractal calculus; generalizations; polymer fluid PDFBibTeX XMLCite \textit{R. Metzler} et al., Fractals 5, No. 4, 597--601 (1997; Zbl 0913.34011) Full Text: DOI References: [1] DOI: 10.1021/ma00024a009 · doi:10.1021/ma00024a009 [2] DOI: 10.1088/0305-4470/28/23/012 · Zbl 0921.73154 · doi:10.1088/0305-4470/28/23/012 [3] DOI: 10.1063/1.528578 · Zbl 0692.45004 · doi:10.1063/1.528578 [4] DOI: 10.1016/0378-4371(94)90064-7 · doi:10.1016/0378-4371(94)90064-7 [5] DOI: 10.1103/PhysRevE.55.99 · doi:10.1103/PhysRevE.55.99 [6] DOI: 10.1142/S0218348X95000497 · Zbl 0868.26004 · doi:10.1142/S0218348X95000497 [7] Gorenflo R., J. Fract. Calc. 8 pp 103– (1995) [8] DOI: 10.1142/S0218348X95000485 · Zbl 0870.58041 · doi:10.1142/S0218348X95000485 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.