You need to review the documentation section on: Getting Started (link). Also see the documentation for Anonymous Functions (link).
Coding your function (as an anonymous function) is straightforward:
y = @(x) a*x.*exp(b*x);
assuming α and β are scalars.
To call it:
a = 1;
b = 2;
x = 0.1:10;
y = @(x) a*x.*exp(b*x);
ye = y(x);
This should get you started.
