Your question asks about how to define this for a non-integer index. However you have not defined how the recurrence would start for a non-integer "index". A recurrence makes mathematical sense only if you can start it in some way. Anyway, MATLAB does not allow non-integer indexes for arrays of any class. That includes cell arrays.
Your idea of a cell array of function handles is pretty much un-workable for what you are asking to do. Sorry. It may look pretty, but in practice the idea is worthless.
Instead, use a loop. I know it seems so terrible. But loops are fine in terms of efficiency. This silly cell array of function handles is still an implicit loop anyway. Using a loop allows you to start the recurrence simply. It allows you to deal with the initial value for that recurrence.
Finally, if you have a current MATLAB release, you might be able to use the memoize function to help you make your code more efficient.
