On The Fractional Domain Analysis of HP TiO2 Memristor Based Circuits with Fractional Conformable Derivative. Issue 1 (1st January 2021) - Banchuin, Rawid
Abstract: For the first time, the physical memristor-based circuits i.e., HP TiO2 memristor-based circuits, of both series and parallel structures, have been extensively analyzed in the fractional domain by means of the state of the art yet simple fractional conformable derivative-based differential equations. Different outcome from the hypotheticalmemory element-based previous researches have been obtained. The dimensional consistencies of the fractional derivatives have also been concerned. The often-cited Joglekar's window function has been adopted for modelling the boundary effect of the memristor and adding more nonlinearity close to the bounds of the memristor's state variable. The formulated fractional differential equations have been solved and the related electrical quantities have been determined. The computational simulations have been performed. The stability analyses of both circuits have also been presented where it has been mathematically verified that only these HP TiO2 memristor-based circuits are stable always due to the boundary effect which does not exist in hypothetical elements assumed in those previous works. We also point out that that only those HP TiO2 memristor-based circuits of order higher than 3 are capable to exhibit the complex dynamics as such memristor lacks the local activity.