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EnglishThe 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.
| Titolo: | Characteristic Roots of a Class of Fractional Oscillators |
| Autori: | |
| Data di pubblicazione: | 2013 |
| Rivista: | |
| 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. |
| Handle: | http://hdl.handle.net/11386/4123455 |
| Appare nelle tipologie: | 1.1.1 Articolo su rivista con DOI |
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