How to fit a function that has significant changes dependent on small changes of some parameters

Hey,

I am fitting a function to data using curve fitting tool in Matlab. The function is very sensitive to two of the fitting parameters (I have totally 6 fitting parameters) and even a very small change in these two parameters make a huge change in the function. Considering this fact, the upper and lower bound of the parameters is quite large. For example, assume parameter L can vary from 0.0035 to 0.0045 while a change in the order of 0.00400006 can make a huge change in the function and make it something different. I have attached an example of how the function changes, when I change L from 0.00400000 to 0.00400006. As a result when I try to have this fitting parameter in my fit and set the lower and upper bound the same as I mentioned, and let's say an start point of 0.004, Matlab only goes true those small increments changes of this parameter and never try the change in order of something like 0.0042 in the parameter. And I have two parameters like this in my fit. Any comments on how can I overcome this challenge?

Thanks in advance!