Can I convert this exponential function in QGIS with Raster Calculator ?
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:
formula in raster calculator looks like:
After click in OK, I got:
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!