Commonly denoted as F_n, the Fibonacci numbers are a sequence that respects the following formula:

F₀=0, F₁ = 1, ... F_n = F_n-1 + F_n-2 (n > 1)

A snapshot of Fibonacci numbers is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

The implementation of Fibonacci numbers via RecursiveAction can be accomplished as follows:

public class FibonacciRecursiveAction extends RecursiveAction {

  private static final Logger logger =
    Logger.getLogger(FibonacciRecursiveAction.class.getName());
  private static final long THRESHOLD = 5;

  private long nr;

  public FibonacciRecursiveAction(long nr) {
    this.nr = nr;
  }

  @Override
  protected void compute() {

    final long n = nr;

    if (n <= THRESHOLD) {
      nr = fibonacci(n);
    } else {
      nr = ForkJoinTask.invokeAll(createSubtasks(n))
        .stream()
        .mapToLong(x -> x.fibonacciNumber())
        .sum();
    }
  }

  private List<FibonacciRecursiveAction> createSubtasks(long n) {

    List<FibonacciRecursiveAction> subtasks = new ArrayList<>();

    FibonacciRecursiveAction fibonacciMinusOne
      = new FibonacciRecursiveAction(n - 1);
    FibonacciRecursiveAction fibonacciMinusTwo
      = new FibonacciRecursiveAction(n - 2);

    subtasks.add(fibonacciMinusOne);
    subtasks.add(fibonacciMinusTwo);

    return subtasks;
  }

  private long fibonacci(long n) {
    logger.info(() -> "Number: " + n 
      + " Thread: " + Thread.currentThread().getName());

    if (n <= 1) {
      return n;
    }

    return fibonacci(n - 1) + fibonacci(n - 2);
  }

  public long fibonacciNumber() {
    return nr;
  }
}

In order to test it, we need the following ForkJoinPool object:

ForkJoinPool forkJoinPool = ForkJoinPool.commonPool();

FibonacciRecursiveAction fibonacciRecursiveAction
  = new FibonacciRecursiveAction(12);
forkJoinPool.invoke(fibonacciRecursiveAction);

logger.info(() -> "Fibonacci: "
  + fibonacciRecursiveAction.fibonacciNumber());

The output for F₁₂ is as follows:

[15:40:46] Number: 5 Thread: ForkJoinPool.commonPool-worker-3
[15:40:46] Number: 5 Thread: ForkJoinPool.commonPool-worker-13
[15:40:46] Number: 4 Thread: ForkJoinPool.commonPool-worker-3
[15:40:46] Number: 4 Thread: ForkJoinPool.commonPool-worker-9
...
[15:40:49] Number: 0 Thread: ForkJoinPool.commonPool-worker-7
[15:40:49] Fibonacci: 144