How to find roots of a polynomial with fractional orders?

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Bilal 2013-12-28

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https://ww2.mathworks.cn/matlabcentral/answers/110913-how-to-find-roots-of-a-polynomial-with-fractional-orders

回答： bahar beladi 2017-2-9

采纳的回答： Roger Stafford

I want to find the roots of the following fractional order polynomial:

P=s^2.1+2*s^1.2+1;

Using the solve() function (solve(s^2.1+2*s^1.2+1)), Matlab finds some roots but how does Matlab compute them? Whats the algorithm?

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Roger Stafford 2013-12-28

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编辑：Roger Stafford 2013-12-28

在 MATLAB Online 中打开

I don't know how 'solve' does it, but here's how I would proceed. Define the variable t = s^(3/10). Then your equation can be rewritten as

t^7+2*t^4+1 = 0

which will have seven roots, (allowing complex numbers.) For each of these, the equation

s^3-t^10 = 0

should have three roots for s, making a total of 21 possible roots, though there could be duplications among them.

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Walter Roberson 2013-12-28

solve(s^(sym(21)/sym(10))==1)

will lead to all the roots, but solve(s^(21/10)==1) will only lead to 1.

Roger Stafford 2013-12-29

To expound at greater length on my statement yesterday as to the possible ways of evaluating, say, s^(12/10), suppose s is equal to -1. Then s^(1/10) can be any one of the ten values, exp(i*k*pi/10), for k = 1,3,5,...,19, and hence s^(12/10) = (s^(1/10))^12 can be any one of the five values, exp(i*k*pi/5), for k = 0,2,4,6,8.

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