documentclass{article}

usepackage{mathtools}

newcommand{abs}[1]{#1}
newcommand{vast}[1]{#1}

begin{document}

  begin{align*}
    f_{y_1,y_2} (y_1,y_2) &= f_{X_1,X_2}(y_1, frac{(1-y_1)}{2} - sqrt{ frac{y_2}{2} -frac{{y_1}^{2}}{2} - frac{(1-y_1)^{2}}{4}} ) abs {J_1}
     + f_{X_1,X_2}(y_1, frac{(1-y_1)}{2} + sqrt{ frac{y_2}{2} -frac{{y_1}^{2}}{2} - frac{(1-y_1)^{2}}{4}} ) abs {J_2}  \
    f_{y_1,y_2} (y_1,y_2) & =  frac{Gamma(alpha_1 +alpha_2)}{Gamma(alpha_1) Gamma(alpha_2)} vast[ (frac{(1-y_1)}{2} - sqrt{R})^{alpha_2 -1} + ( frac{(1-y_1)}{2}+ sqrt{R})^{alpha_2 -1} vast]\
    end{align*}

end{document}