Can I convert this exponential function in QGIS with Raster Calculator ?

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Yes, you can.

Assuming alpha = 0.5, beta = 3.2 and 2.71828 for Euler's number, the formula in raster calculator of QGIS would be:

2.71828 ^ (-0.5*"NDVI@"/(3.2 - "NDVI@"))

Testing it with next NDVI raster:

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formula in raster calculator looks like:

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After click in OK, I got:

enter image description here

Raster values were also calculated with the help of a manual calculator and they match the formula (visualized with Value Tool plugin of QGIS). It works!

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