I found the solution myself. The init_guess in vpasolve did somehow not help (maybe the expression was faulty?)
BUT assume and assumeAlso brought the solution:
syms f a b
f = a*x^(-b);
assume(b>3);
assumeAlso(a>35);
%a=38.76;
%b=3.969;
%F=int(f,x)
eqns=[int(f,x,[3 Inf]) == 1/2,int(f,x,[9/2 Inf])==15/100];
vars = [a b];
[sola, solb] = vpasolve(eqns,vars)
sola =
38.759579642286119630010875007585
solb =
3.9693622959161180276359691433877