Test task dependence of the optimal fractional order

Determine whether the optimal fractional order is determined by a task’s temporal-memory structure or is specific to closed-loop control tasks.

Background

Two independent studies reported an optimal fractional order near 0.5 for cart-pole control, while another benchmark involving physiological prediction reported an optimum near 0.1. The review identifies this discrepancy as the central unresolved question in the software portion of the field.

A second task with a different temporal structure would test whether the apparent order optimum generalizes across workloads or instead reflects properties of control problems.

References

Whether the optimum is a property of the task's memory structure or of control problems in particular is now the sharpest open question in the software half of this field, and it is answerable with a laptop.

— Fractional-order hardware for neuromorphic computing: Is the order really the problem?  (2609.10882 - Teuscher, 9 Sep 2026) in Section 7.3, “Gaps, stated as questions”