A comparative mathematical analysis of RL and RC electrical circuits via Atangana-Baleanu and Caputo-Fabrizio fractional derivatives

Abro, Kashif Ali; Memon, Anwar Ahmed; Uqaili, Muhammad Aslam

doi:10.1140/epjp/i2018-11953-8

Cited by 91 publications

(22 citation statements)

References 25 publications

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“…They claimed that new strange behaviors of the attractors were not possible by only classical differentiations. In short, the study can be continued for the charming and effective role of fractional calculus in applied engineering problems, 20–31 but we include here recent attempt in categorically as epidemiology, 32–39 heat and mass transfer, 40–44 fluid mechanics, 45–47 nanofluids, 48–51 and electrical engineering 52–55 . Motivating by above discussion, our aim is to propose the controlling analysis and coexisting attractors provided by memristor through highly nonlinear for mathematical relationships of governing differential equations.…”

Section: Introductionmentioning

confidence: 99%

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

Abro

Atangana

2020

Math Methods in App Sciences

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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.

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Section: Introductionmentioning

confidence: 99%

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

Abro

Atangana

2020

Math Methods in App Sciences

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“…Fractional-order operators have successfully been applied to model a number of mathematical problems arising from the fields like physics, chemistry, biology, ecology, finance, and engineering. Many such mathematical models have been proposed and analyzed by using different fractional-order operators as can be found in the recent studies [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. It is well known that Riemann-Liouville and Caputo-type fractional operators have singular type of kernels in the integrands of their definitions.…”

Section: Introductionmentioning

confidence: 99%

Existence theory and numerical simulation of HIV-I cure model with new fractional derivative possessing a non-singular kernel

Aliyu

İnç

et al. 2019

Adv Differ Equ

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In this research work, a mathematical model related to HIV-I cure infection therapy consisting of three populations is investigated from the fractional calculus viewpoint. Fractional version of the model under consideration has been proposed. The proposed model is examined by using the Atangana-Baleanu fractional operator in the Caputo sense (ABC). The theory of Picard-Lindelöf has been employed to prove existence and uniqueness of the special solutions of the proposed fractional-order model. Further, it is also shown that the non-negative hyper-plane R 3 + is a positively invariant region for the underlying model. Finally, to analyze the results, some numerical simulations are carried out via a numerical technique recently devised for finding approximate solutions of fractional-order dynamical systems. Upon comparison of the numerical simulations, it has been demonstrated that the proposed fractional-order model is more accurate than its classical version. All the necessary computations have been performed using MATLAB R2018a with double precision arithmetic.

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“…In [18], the CF fractional derivative was used for numerical approach of the Fokker-Planck equation using Ritz approximation. A mathematical comparative analysis of RL and RC electrical circuits using AB and CF fractional derivatives was recently done in [19]. Mustafa et al [20] explored the dynamics of the cancer treatment model with the CF fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

A fractional order pine wilt disease model with Caputo–Fabrizio derivative

et al. 2018

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A Caputo-Fabrizio type fractional order mathematical model for the dynamics of pine wilt disease (FPWD) is presented. The basic properties of the model are investigated. The existence and uniqueness of the solution for the proposed FPWD model are given via the fixed point theorem. The numerical simulations for the model are obtained by using particular parameter values. The non-integer order derivative provides more flexible and deeper information about the complexity of the dynamics of the proposed FPWD model than the integer order models established before.

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A comparative mathematical analysis of RL and RC electrical circuits via Atangana-Baleanu and Caputo-Fabrizio fractional derivatives

Cited by 91 publications

References 25 publications

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

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

Existence theory and numerical simulation of HIV-I cure model with new fractional derivative possessing a non-singular kernel

A fractional order pine wilt disease model with Caputo–Fabrizio derivative

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