See the article "Anonymous Functions" in the MATLAB help. You must pass all parameters to the anonymous function as inputs, so maybe
Ra = @(x,Pr,g,L,betha,T_1,v) Pr*(g*L^3*betha*(x-T_l))/v^2;
Unless you want to declare all the parameters as globals.
Also, do not overwrite your function handle for alpha_k. Try:
alpha_k_output = alpha_k(xsol);
alpha_k will also need all those parameters that Ra needs unless you want them to be global. Try a smaller example to debug how you are using alpha_k and Ra first before trying to use them in the newton_raphson local function.