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This paper exhibits a third-order Newton process for approximating , the general fractional capacitor, for any integer > 1. The approximation is based on predistortion of the algebraic expression . The resulting approximation in real variables (resistive networks) has the unique property of preserving upper and lower approximations to the th root of the real number . Any Newton process which possesses this property is regular. The real variable theory of regular Newton processes is presented because motivation lies in the real variable domain. Realizations of 1/3 and 1/4 order fractional capacitor approximations are presented.