Question: How can I calculate a series with expressions as powers

I would like to calculate the power series solution of a set of ODEs. However, I know that this power series will contain non-integer coefficients, which are dependent on a (rational) parameter of the system, α. I'm solving the ODE by power series in the usual way, that is, by defining each of the solution variables as a function with the first few terms of their power series (with unknown coefficients), substituting these into the ODEs, and finding a series of the ODE which should be of the form:

 a + b*x + c*x^α + d*x^(2*α-1) + e * x^2 ... = 0

where the coefficients a,b,c,d,e,... are functions of α and of the unknown coefficients of the solution variable power series. As demonstrated in the equation above, I have some integer powers and some which are functions of α. By equating the coefficients a,b,c,... to zero, I hope to find the coefficients of the solution variable power series, as functions of α.

To calculate the series above, I currently have to use subs to substitute a specified rational number for α, since the series command does not function with arbitrary powers. However, the subs command also substitutes for α in the coefficients a,b,c,d,e,..., so I am unable to get a,b,c,... as functions of α. I have tried algsubs, but this does not seem to work with a-priori-unknown powers either.

How can I substitute a value for α ONLY where it occurs in a power of x, but leave the symbol as α when it occurs in a cofficient? Or is there another way of solving this problem?