5. Conclusion
This manuscript is investigated to present the fractal-fractional model
based on highly non-linear for mathematical model of memristor in terms
of fractal-fractional differential operator so called Atangana-Baleanu,
Caputo-Fabrizio and Caputo fractal-fractional differential operator. The
numerical solutions for mathematical model of memristor have extensively
been discussed by means of Adams-Bashforth-Moulton method. With the help
of numerical schemes of fractal-fractional differential operators,
chaotic behavior of memristor under three criteria is discussed 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. Such analysis of attractors is
simulated via MATLAB. At the end, chaotic behaviors of memristor suggest
that newly presented Atangana-Baleanu, Caputo-Fabrizio and Caputo
fractal-fractional differential operator has generates significant
results as compared with classical approach.