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Mathematical analysis of memristor through fractal‐fractional differential operators: A numerical study
Author(s) -
Abro Kashif Ali,
Atangana Abdon
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6378
Subject(s) - memristor , fractal , mathematics , attractor , fractional calculus , chaotic , differential equation , operator (biology) , nonlinear system , differential operator , mathematical analysis , computer science , physics , artificial intelligence , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
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.