The fundamental theorem of algebra determines the number of characteristic roots of an ordinary differential equation of integer order. Thismay cease to be true for a differential equation of fractional order.Theresults given in this paper suggest that the number of the characteristic roots of a class of oscillators of fractional order may in general be infinitely great. Further, we infer that it may also be the case for the characteristic roots of a differential equation of fractional order greater than 1.The relationship between the range of the fractional order and the locations of characteristic roots of oscillators in the complex plane is considered.
Characteristic Roots of a Class of Fractional Oscillators
CATTANI, Carlo;
2013
Abstract
The fundamental theorem of algebra determines the number of characteristic roots of an ordinary differential equation of integer order. Thismay cease to be true for a differential equation of fractional order.Theresults given in this paper suggest that the number of the characteristic roots of a class of oscillators of fractional order may in general be infinitely great. Further, we infer that it may also be the case for the characteristic roots of a differential equation of fractional order greater than 1.The relationship between the range of the fractional order and the locations of characteristic roots of oscillators in the complex plane is considered.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
