Can I install my handrail into composite decking material.

Yes you can.  Composite decking itself is not strong enough alone.  What you will want to do is provide wood blocking under the composite decking so you can screw through the handrail base plate, through the composite decking and into the wood blocking below.  This could be blocking you intentionally place there or into the wood stair stringers.  The other option would be to bolt through the base plate and composite decking and use large washers and nuts below the composite decking.

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