Abstract In this work, a novel generalized mathematical model of fractional‐order memristor with fully explicit memory description has been proposed. For obtaining such full explicit memory description, the Atangana‐Baleanu fractional derivative in Liouville‐Caputo sense, which employs a nonsingular kernel, has been adopted as the mathematical basis. The proposed model has been derived without regarding to any specific conventional memristor. A comparison with the singular kernel fractional derivative‐based model has been made. The behavioral analysis of the fractional‐order memristor based on the proposed model has been performed, where both DC and AC stimuli have been considered. In addition, its application to the practical fractional‐order memristor‐based circuit and its extension to the fractional‐order memreactance have also been shown. Unlike the singular kernel fractional derivative‐based model, a fully explicit memory description can be obtained by ours. Many other interesting results that are contradict to the previous singular kernel fractional derivative‐based ones, e.g., the fractional‐order memristor that can be locally active, have been demonstrated. The abovementioned extension can be conveniently performed. In summary, this is the first time that a nonsingular kernel fractional derivative has been applied to the fractional‐order memristor modeling and the resulting model with a fully explicit memory description has been proposed. The proposed model is also highly generic, applicable to the practical circuit, and extendable to the fractional‐order memreactance.
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