Structural Invalidity of the Modified Chain Rule in He et al.

This work re-examines the modified chain-rule identity proposed by He, Elagan, and Li (2012). Although they correctly demonstrate that the previously used chain rule is invalid, the replacement formula containing a geometric scaling factor does not resolve the underlying analytic inconsistency. Both identities share the same local-product structure, which is incompatible with the integral definition of Jumarie’s modified Riemann–Liouville derivative. Multiple counterexamples show that no fixed geometric constant can make the modified identity valid. Consequently, the reduction procedure in Section 5 of the original paper lacks mathematical justification, and subsequent works relying on this chain rule should be revisited. This clarification helps prevent further propagation of incorrect chain-rule assumptions in fractional-calculus research.