Mathematical analysis of memristor through fractal-fractional differential operators: A numerical study

The newly generalized energy storage component, namely, memristor, which is a fundamental circuit element so called universal charge-controlled mem-element, is proposed for controlling the analysis and coexisting attractors. The governing differential equations of memristor are highly nonlinear for mathematical relationships. The mathematical model of memristor is established in terms of newly defined fractal-fractional differential operators so called Atangana-Baleanu, Caputo-Fabrizio, and Caputo fractal-fractional differential operator. A novel numerical approach is developed for the governing differential equations of memristor on the basis of Atangana-Baleanu, Caputo-Fabrizio, and Caputo fractal-fractional differential operator. We discussed chaotic behavior of memristor under three criteria such as (i) varying fractal order, we fixed fractional order; (ii) varying fractional order, we fixed fractal order; and (ii) varying fractal and fractional orders simultaneously. Our investigated graphical illustrations and simulated results via MATLAB for the chaotic behaviors of memristor suggest that newly presented Atangana-Baleanu, Caputo-Fabrizio, and Caputo fractal-fractional differential operators generate significant results as compared with classical approach.