Constructing a Function with a given Singularity

Dear All,
I hope this is not too off topic.
I do not know if maxima can help me at all, but I would like to give it 
a try. I need to build a function of a power-law of x with the following 
asymptotic behavior for large x

f(x^alpha)--> 0, if alpha=1,
f(x^alpha)--> constant, if alpha in (1,1/3]

Does anybody have any idea about how to do this in maxima?
I repeat that I need a function of x^alpha; I cannot e.g. express 
f(x^alpha)=alpha*g(x^alpha), as alpha can appear only in the expression 
x^alpha. Does anybody have any idea about how to achieve that?
Many thanks

Lorenzo