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Mathematical Analysis of Memristor through Fractal-Fractional Differential Operator: A Numerical Study
  • Kashif Ali Abro,
  • Abdon Atangana
Kashif Ali Abro
Mehran University of Engineering and Technology
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Abdon Atangana
University of the Free State
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Abstract

The newly generalized energy storage component namely memristor 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 non-linear 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 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 operator has generates significant results as compared with classical approach.

Peer review status:ACCEPTED

24 Jan 2020Submitted to Mathematical Methods in the Applied Sciences
25 Jan 2020Submission Checks Completed
25 Jan 2020Assigned to Editor
27 Jan 2020Reviewer(s) Assigned
03 Mar 2020Review(s) Completed, Editorial Evaluation Pending
05 Mar 2020Editorial Decision: Revise Minor
15 Mar 20201st Revision Received
15 Mar 2020Submission Checks Completed
15 Mar 2020Assigned to Editor
15 Mar 2020Editorial Decision: Accept