The effects of continuously varying the fractional differential order of chaotic nonlinear systems (Q1125136)

The authors describe results of a numerical study on various bifurcation phenomena including the appearance of chaotic behavior for some fractional-order differential equations. For example, they study the equation \[ D^{2+q}x=-D^2x+xDx-0.9x-0.4, \tag{1} \] where \(q\) varies from 0 to 1. In (1), \(D^px\) denotes the derivative of \(x\) of order \(p\), and fractional derivatives (with \(p\) noninteger) are defined following the approach of \textit{K. B. Oldham} and \textit{Spanier} [The fractional calculus. New York, London: Academic Press (1974; Zbl 0292.26011)].