Functionality of circuit via modern fractional differentiations

Abro, Kashif Ali; Memon, Ali Asghar; Memon, Anwar Ahmed

doi:10.1007/s10470-018-1371-6

Cited by 50 publications

(14 citation statements)

References 31 publications

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“…Although [2][3][4][5][6] has completed a great deal of work on dynamic modeling of influenza, it is limited to ordinary differential equations. However, currently, it has been found that the use of fractional differential equations to model many different fields of phenomena has been very successful [7][8][9][10][11][12][13][14][15][16][17][18]. For instance, in mathematical epidemiology, Ebola virus epidemic has been modeled with fractional-order differential equations by [19].…”

Section: Introductionmentioning

confidence: 99%

Analysis and Optimal Control of Fractional-Order Transmission of a Respiratory Epidemic Model

Yaro

Apeanti

Akuamoah

et al. 2019

Int. J. Appl. Comput. Math

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The World Health Organization is yet to realise the global aim of achieving future-free and eliminating the transmission of respiratory diseases such as H1N1, SARS and Ebola since the recent reemergence of Ebola in the Democratic Republic of Congo. In this paper, a Caputo fractional-order derivative is applied to a system of non-integer order differential equation to model the transmission dynamics of respiratory diseases. The nonnegative solutions of the system are obtained by using the Generalized Mean Value Theorem. The next generation matrix approach is used to obtain the basic reproduction number R 0 . We discuss the stability of the disease-free equilibrium when R 0 < 1, and the necessary conditions for the stability of the endemic equilibrium when R 0 > 1. A sensitivity analysis shows that R 0 is most sensitive to the probability of the disease transmission rate. The results from the numerical simulations of optimal control strategies disclose that the utmost way of controlling or probably eradicating the transmission of respiratory diseases should be quarantining the exposed individuals, monitoring and treating infected people for a substantial period.

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Section: Introductionmentioning

confidence: 99%

Analysis and Optimal Control of Fractional-Order Transmission of a Respiratory Epidemic Model

Yaro

Apeanti

Akuamoah

et al. 2019

Int. J. Appl. Comput. Math

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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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“…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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Functionality of circuit via modern fractional differentiations

Cited by 50 publications

References 31 publications

Analysis and Optimal Control of Fractional-Order Transmission of a Respiratory Epidemic Model

Analysis and Optimal Control of Fractional-Order Transmission of a Respiratory Epidemic Model

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

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