Curve fitting a part of a bigger curve using cftool

I have a big data curve with more than 200000 data points. Now I want to fit certain parts of a curve which has a slow transient response and I want to fit it with a custom equation to find different variables. I want to know exactly how to do it . I will attach the picture of the bigger and the smaller curve here.

Fig.1 This first curve shows the bigger curve and I have marked the part of the curve where I need to fit with an equation. I have zoomed in that part in the second picture.

I want to fit this part of the curve (Fig.2) with a custom equation and find the parameters of that equation after completing an optimal fit. Adding to that I need to do this for every such curves (all the spikes in the Fig.1 above) and find the parameters after fitting the custom Equation. Can anyone explain to me how to do it.

Fig.2