Scalable algorithms with certificates for fractional differential games

Develop scalable computational algorithms for fractional differential games together with a priori and a posteriori certificates that quantitatively relate approximation errors of fractional-memory surrogates (such as diffusive or Oustaloup realizations) to game-theoretic suboptimality gaps.

Background

The survey discusses practical solution routes via augmented-state (diffusive/CRONE) approximations to Markovize memory for game solvers.

A key unresolved need is principled certification linking approximation error in the fractional operator to the resulting equilibrium’s suboptimality and robustness.

References

Open questions. Refinements are still needed on: (a) Isaacs–type conditions under memory; (b) existence/uniqueness for general–sum FO games; (c) verifiable sufficient conditions for Stackelberg equilibria in FDGs; and (d) scalable algorithms with a priori/a posteriori certificates that couple fractional–approximation error with game–theoretic suboptimality.

— Fractional Calculus in Optimal Control and Game Theory: Theory, Numerics, and Applications -- A Survey (2512.12111 - Mojahed et al., 13 Dec 2025) in Section 4, Subsection “Fractional Differential Games (FDGs)”, Open questions paragraph