deletions | additions       diff --git a/Kinetic model with dynamic disorder.tex b/Kinetic model with dynamic disorder.tex  index e7350dd..3297b8d 100644  --- a/Kinetic model with dynamic disorder.tex  +++ b/Kinetic model with dynamic disorder.tex 
...
\mathcal{J}_{KWW}(\Delta{t}) =  \frac{\Delta tC_A(0)^{2\beta}\beta^{2}\omega^{2\beta}t^{2\beta-1}}{2\beta-1}\bigg|_{t_i}^{t_f}  \end{equation}  This form shows the $\frac{1}{2}$ $\beta$ valuse must be evaluated seperately which yields the final result for comparison. And when $\beta=\frac{1}{2}$, When $\beta=\tfrac{1}{2}$,  \begin{equation}  \mathcal{J}_{KWW}(\Delta{t}) = \Delta t C_A(0)\beta^2\omega^{2\beta} \ln(t)\big|_{t_i}^{t_f}  \end{equation}