Dear Sardar, there are a large number of numerical procedures to perform this fit.  For small problem like this, Newton's method or Gauss-Newton methods are recommended.

In short, it is a least-squares procedure, where you write down the analytical form of the sum of square error between predicted and data y values as a function of unknown variables, then optimize this function by setting the derivative of this function to zero.

For Newton's method, you will need to derive the analytical form of the first and second derivative of y with respect to each unknown, which should be fairly straightforward for this particular problem.  For Gauss-Newton it is even simpler, you'll only need to derive first derivatives.

In general non-linear optimizations are iterative.  That means you will need to perform an approximate procedure multiple times to obtain solutions that hopefully become more and more accurate and approach the best value.  

There are often problems of multiple local-minima.  You would want to start with a reasonably good set of parameters to get to the optimal values.

I made this R code for you where you can try different optimization algorithms and see how general purpose optimization works in practice.

Play around with the parameters to the optim function: https://stat.ethz.ch/R-manual/R-devel/library/stats/html/optim.html

Cheers

Code

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