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I want to calculate FAPAR in different land cover types using max and min value of NDVI. I have a raster image with 9 Land cover types and max, min value of NDVI in each land cover type. But I don't know the way how to calculate it in different LC types from NDVI image. what kind of function can be used to do this. what software is more useful for this kind of calculation?

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My understanding of fAPAR is that it is a replacement for NDVI, and not something which is derivable from an existing NDVI image. You can find FAPAR scenes to download, otherwise you'd probably need to implement the algorithm based on per-channel scenes. I see one student project which estimated fAPAR as fAPAR = NDVI * 1.25 – 0.025 but I'd take this calculation with a grain of salt.

For your second question of looking at the values within land cover types, you can use Zonal Statistics assuming you're sticking with ArcGIS.

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+1 The student project doesn't provide any basis for that relationship. However, Myneni & Williams in a 2004 paper provide some (qualified) hope: "In situ fAPAR and normalised differential vegetation index (NDVI) for three different vegetation types showed a strong linear relationship... The fAPAR/NDVI relations found here, however, do not apply on a global scale but are only valid for similar sun-sensor view geometry and soil colour." –  whuber May 22 '11 at 21:21
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