Memfractance: A Mathematical Paradigm for Circuit Elements with Memory

Memristor, the missing fourth passive circuit element predicted forty years ago by L. O. Chua was recognized as a nanoscale device in 2008 by researchers of a H.P. Laboratory. Recently the notion of memristive systems was extended to capacitive and inductive elements, namely, memcapacitor and meminductor whose properties depend on the state and history of the system. In this paper, we use fractional calculus to generalize and provide a mathematical paradigm for describing the behavior of such elements with memory. In this framework we extend Ohm’s law to the generalized Ohm’s Law and prove it.