New complex wave patterns to the electrical transmission line model arising in network system

Gao, Wei; Senel, Mine; Yel, Gülnur; Başkonuş, Hacı Mehmet; Şenel, Bilgin

doi:10.3934/math.2020125

Cited by 80 publications

(13 citation statements)

References 25 publications

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“…The Eqs. (13), (14), (16), and (17) providing the same values i.e, ψ = 1 and e = 1 2 , indicated that if the visitors visit the particular city or no visitors there in the concern city the spreading ratio of the disease remain same from the fixed values taken both population. These fixed values of both the population ψ and e create a perception that visitors have not a key role in this epidemic disease which spread in particular region of the "Wahan" city.…”

Section: Methodology For Our Modelmentioning

confidence: 94%

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Using caputo-fabrizio derivative for the transmission of mathematical model epidemic Corona Virus

Tahir

Zaman

Shah

2020

SeMA

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Just in a week a rapidly spreading corona virus which was originated in Wuhan, city of China, infected more than 20,000 people and also killed at least 427 people in that week worldwide. Corona virus is transmissible and spreading from person to person, while the Chinese commanded authorities are scrambling to treat a flood of new patients in Chines successfully. The said Corona virus has been spread from an initial outbreak in Wuhan, city of China, and invade 25 other worldwide countries. In this article, we considered the mathematical model (Chen et al. Infect Dis Poverty, https://doi.org/10.1186/s40249-020-00640-3) in which Bats-Hosts-Reservoir-People and their transmission was taken, while we introduced the population of susceptible Bats and visitors to Wuhan city or any country in same mathematical model. Now we studying two types of populations first Bats-Hosts-Reservoir-People (Chen et al. Infect Dis Poverty, https://doi.org/10.1186/s40249-020-00640-3, also introducing susceptible Bats and second visitors to Wuhan city, china or any country in the same model. We used Caputo-Fabrizio derivative with provided result that the addition of susceptible Bats and visitors are not responsible in spread of infection. The numerical result also supported our model.

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Section: Methodology For Our Modelmentioning

confidence: 94%

“…The people are awarded from different methods, and control strategies to make possible precautions against Corona virus. Here the main aim is to estimate positivity, equilibrium, and Boundedness of these models [ 11 , 13 , 16 , 27 ]. The recent and new ideas was also discussed in [ 1 – 3 , 5 , 14 , 19 , 25 , 26 ].…”

Section: Introductionmentioning

confidence: 99%

Using caputo-fabrizio derivative for the transmission of mathematical model epidemic Corona Virus

Tahir

Zaman

Shah

2020

SeMA

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“…With the help of Equations (26)- (29) and by putting the value of u(x, t) and their fractional derivative, we get the residual function as follows:…”

Section: Proposed Algorithmsmentioning

confidence: 99%

“…This advection term represents the bulk flow of motion of fluid or physical quantity. Some recent research of fractional mathematical models can be found in such as disease in pregnant women, 26 Schistosomiasis disease arising in biological phenomena, 27 phi-four equation, 28 electrical transmission line model, 29 boundary value problem, 30 and rheological models. 31 In the last few decades, the use of standard diffusive constitutive models like Fick's law or Fourier has been used extensively.…”

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confidence: 99%

Numerical solution of two‐dimensional time fractional cable equation with Mittag‐Leffler kernel

Kumar¹,

Băleanu

2020

Math Methods in App Sciences

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The main motive of this article is to study the recently developed Atangana‐Baleanu Caputo (ABC) fractional operator that is obtained by replacing the classical singular kernel by Mittag‐Leffler kernel in the definition of the fractional differential operator. We investigate a novel numerical method for the nonlinear two‐dimensional cable equation in which time‐fractional derivative is of Mittag‐Leffler kernel type. First, we derive an approximation formula of the fractional‐order ABC derivative of a function tk using a numerical integration scheme. Using this approximation formula and some properties of shifted Legendre polynomials, we derived the operational matrix of ABC derivative. In the author of knowledge, this operational matrix of ABC derivative is derived the first time. We have shown the efficiency of this newly derived operational matrix by taking one example. Then we solved a new class of fractional partial differential equations (FPDEs) by the implementation of this ABC operational matrix. The two‐dimensional model of the time‐fractional model of the cable equation is solved and investigated by this method. We have shown the effectiveness and validity of our proposed method by giving the solution of some numerical examples of the two‐dimensional fractional cable equation. We compare our obtained numerical results with the analytical results, and we conclude that our proposed numerical method is feasible and the accuracy can be seen by error tables. We see that the accuracy is so good. This method will be very useful to investigate a different type of model that have Mittag‐Leffler fractional derivative.

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“…Many nonlinear physical phenomena in nature are described by nonlinear partial differential equations (PDEs). For deliberative speedy development of symbolic computation systems [1][2][3][4][5], the search for the exact solutions of nonlinear equations has attracted a lot of attention [6][7][8][9] as the exact solutions make it possible to research nonlinear physical phenomena comprehensively and facilitate testing the numerical schemes [10][11][12][13][14]. In the last two decades, various approaches have been proposed and applied to the nonlinear equations of PDEs, such as homogeneous balance method [15,16], extended tanh-function method [17][18][19][20], Jacobi elliptic function expansion method [21], simple equation method [22][23][24], (G/G′)-expansion method [25][26][27], Hirotas bilinear method [28], Exp function method [29], general projective Riccati equation method [30], modified simple equation method [31][32][33], improved direct algebraic technique, [34,35], auxiliary scheme [36] and so on [37][38][39][40][41][42]…”

Section: Introductionmentioning

confidence: 99%

Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water

2020

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This article scrutinizes the efficacy of analytical mathematical schemes, improved simple equation and exp(-\text{Ψ}(\xi ))-expansion techniques for solving the well-known nonlinear partial differential equations. A longitudinal wave model is used for the description of the dispersion in the circular rod grounded via transverse Poisson’s effect; similarly, the Boussinesq equation is used for extensive wave propagation on the surface of water. Many other such types of equations are also solved with these techniques. Hence, our methods appear easier and faster via symbolic computation.

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New complex wave patterns to the electrical transmission line model arising in network system

Cited by 80 publications

References 25 publications

Using caputo-fabrizio derivative for the transmission of mathematical model epidemic Corona Virus

Using caputo-fabrizio derivative for the transmission of mathematical model epidemic Corona Virus

Numerical solution of two‐dimensional time fractional cable equation with Mittag‐Leffler kernel

Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water

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