How to use collect with arbitrary powers?

Question

I want to use of collect for this code:

x^α (9/(100 α κ Gamma[α]) - x/(
    100 (α + α^2) κ Gamma[α]) - Subscript[
    a, 0]/(α Gamma[α])) + 
 x^(2 α) ((
    2^(2 - 2 α)
      Cos[π α] Gamma[1/2 - α] Subscript[a, 0])/(
    5 Sqrt[π] α κ Gamma[α]) - (
    x Subscript[a, 0])/(10 κ Gamma[2 + 2 α]) - (
    x Gamma[2 + α] Subscript[a, 0])/(
    10 α κ Gamma[α] Gamma[2 + 2 α]) - (
    2^(-2 α) Sqrt[π] Subscript[a, 1])/
    Gamma[1/2 + α])

so that we have power to form of

x   x^α   x^(2α)  x^(3α)  ...

that

I have reviewed these answers Collect1 collect2 but I did not understand. Any suggestion?

How is this different than your last question? You've asked a lot of questions about this in the last few days, and it seems you haven't gotten an acceptable answer. Perhaps you need to give more details. Anyway, what's wrong with Collect[expr, x^_]? — march, Apr 09 '16 at 15:03
@march I deleted that question, because that is not my opinion. This question is not the same with it. — Bahram Agheli, Apr 09 '16 at 15:12
Neither of the two answers cited in the question relate to Collect. As suggested earlier by @march, use Collect[exp, x^α, Simplify] or some variant of it. — bbgodfrey, Apr 09 '16 at 17:42
@bbgodfrey I used this code but "Simplify" is not good, and " x" is not in collect. I want "Ax+B x^α+C*x^2α + . . . ". — Bahram Agheli, Apr 09 '16 at 17:48
The expression contain terms proportional to (x^α), x^(2 α), x^(1 + α), and x^(1 + 2 α), so it cannot look like what your want. — bbgodfrey, Apr 09 '16 at 18:02

score 1 · Answer 1 · answered Apr 09 '16 at 18:59

expr = x^α (9/(100 α κ Gamma[α]) - 
      x/(100 (α + α^2) κ Gamma[α]) - 
      Subscript[a, 0]/(α Gamma[α])) + 
   x^(2 α) ((2^(2 - 2 α) Cos[π α] Gamma[
          1/2 - α] Subscript[a, 
          0])/(5 Sqrt[π] α κ Gamma[α]) - (x \
Subscript[a, 0])/(10 κ Gamma[2 + 2 α]) - (x Gamma[
          2 + α] Subscript[a, 
          0])/(10 α κ Gamma[α] Gamma[
          2 + 2 α]) - (2^(-2 α) Sqrt[π] Subscript[a, 1])/
       Gamma[1/2 + α]);

If your intent is to allow the coefficients to contain terms with an x factor

TraditionalForm[expr2 = Collect[expr, x^α, FullSimplify]]

If the intent is to display terms with the form x^(m*α + n)

TraditionalForm[expr3 = Collect[#, x, FullSimplify] & /@ expr2]

How to use collect with arbitrary powers?

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