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The experimental study of two kinds of electrical circuits, a domino ladderand a nested ladder, is presented. While the domino ladder is known and alreadyappeared in the theory of fractional-order systems, the nested ladder circuitis presented in this article for the first time. For fitting the measured data,a new approach is suggested, which is based on using the Mittag-Lefflerfunction and which means that the data are fitted by a solution of aninitial-value problem for a two-term fractional differential equation. Theexperiment showed that in the frequency domain the domino ladder behaves as asystem of order 0.5 and the nested ladder as a system of order 0.25, which isin perfect agreement with the theory developed for their design. In the timedomain, however, the order of the domino ladder is changing from roughly 0.5 toalmost 1, and the order of the nested ladder is changing in a similar manner,from roughly 0.25 to almost 1; in both cases, the order 1 is never reached, andboth systems remain the systems of non-integer order less than 1. Both studiedtypes of electrical circuits provide the first known examples of circuits,which are made of passive elements only and which exhibit in the time domainthe behavior of variable order.

Experimental evidence of variable-order behavior of ladders and nested ladders