Origin of the Curie-von Schweidler law and the fractional capacitor from time-varying capacitance

The paper derives Rİ + (I − θ VC)/(C0 + θ t) = 0 and then integrates to obtain I(t) = (IR − θ VC)[1 + (θ/C0)t]^{−1/(Rθ)} + θ VC (its Eq. (6)), but this integration implicitly treats VC as constant and drops the −θ V̇C term; it therefore misses an extra factor in the exponent and yields an incorrect DC plateau. Using V̇C = (I − θ VC)/(C0 + θ t) and V0 = R I + VC, the correct elimination leads to a linear ODE in I(t) whose exact solution is I(t) = θ V0/(1 + R θ) + (I(0+) − θ V0/(1 + R θ))[(C0 + θ t)/C0]^{−(1+Rθ)/(Rθ)}. This matches the candidate's derivation and shows the paper's Eq. (6) corresponds only to the auxiliary approximation VC(t) ≈ VC = const. Consequently, the paper's claimed exact identification of UDR/CvS parameters follows from an unjustified approximation, whereas the candidate clearly separates the exact result from the approximate UDR form and identifies parameters under that approximation. See the paper’s derivation around Eq. (6) and its use to claim the CvS law and parameter identifications a, b, α, τ, Cf as exact .