Using reproducing kernel for solving a class of time-fractional telegraph equation with initial value conditions

Wang, Yulan; Du, Mingjing; Chaolu, Temuer; Tian, Dan

doi:10.1080/00207160.2017.1322693

Cited by 12 publications

(8 citation statements)

References 23 publications

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“…Problem 4.1. [3,16,17] Consider the time fractional TDE having non-polynomial exact solution…”

Section: Numerical Problemsmentioning

confidence: 99%

“…From Figure 1, this solution takes five decimal accuracies (10 −5 ). Besides, Table 1 compares the computation results of E RM S in terms of the proposed (PM), the local meshless (LMM) [16], the radial basis function (RBF) [3] and the reproducing kernel (RKM) [17] methods. It can be noticed from Table 1 that the proposed method achieves far more accurate approximation than the other methods with respect to the low computation limit (N) and each specified fractional derivative.…”

Section: Numerical Problemsmentioning

confidence: 99%

“…Hosseini et al [3] have deployed the radial basis function method for time fractional TDEs. Wang et al [17] have solved a class of time fractional TDE subjected to the initial conditions by implementing the reproducing kernel method. Pandey and Mishra [18] have established the numerical simulation of the time-space fractional TDEs using the homotopy analysis method and Sumudu transform.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A novel numerical implementation for solving time fractional telegraph differential equations having multiple space and time delays via Delannoy polynomial

Kürkçü

2021

MANAS Journal of Engineering

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This paper is concerned with solving numerically the time fractional telegraph equations having multiple space and time delays by proposing a novel matrix-collocation method dependent on the Delannoy polynomial. This method enables easy and fast approximation tool consisting of the matrix expansions of the functions using only the Delannoy polynomial. Thus, the solutions are obtained directly from a unique matrix system. Also, the residual error computation, which involves the same procedure as the method, provides the improvement of the solutions. The method is evaluated under some valuable error tests in the numerical applications. To do this, a unique computer module is devised. The present results are compared with those of the existing methods in the literature, in order to oversee the precision and efficiency of the method. One can express that the proposed method admits very consistent approximation for the equations in question.

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“…Problem 4.1. [3,16,17] Consider the time fractional TDE having non-polynomial exact solution…”

Section: Numerical Problemsmentioning

confidence: 99%

Section: Numerical Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A novel numerical implementation for solving time fractional telegraph differential equations having multiple space and time delays via Delannoy polynomial

Kürkçü

2021

MANAS Journal of Engineering

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“…Hashemi and Baleanu [2] proposed a numerical method for the solution of TFTE using the Caputo fractional derivative in time direction, a combination of a group preserving scheme and the method of line for spatial direction. The reproducing kernel method has been presented for the solution of TFTE with initial boundary conditions by Wang et al [20]. Wang and Mei [21] proposed a method for solving TFTE via the Legendre spectral Galerkin method and generalized finite difference scheme.…”

Section: Application and Literature Reviewmentioning

confidence: 99%

Extended cubic B-splines in the numerical solution of time fractional telegraph equation

et al. 2019

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A finite difference scheme based on extended cubic B-spline method for the solution of time fractional telegraph equation is presented and discussed. The Caputo fractional formula is used in the discretization of the time fractional derivative. A combination of the Caputo fractional derivative together with an extended cubic B-spline is utilized to obtain the computed solutions. The proposed scheme is shown to possess the unconditional stability property with second order convergence. Numerical results demonstrate the applicability, simplicity and the strength of the scheme in solving the time fractional telegraph equation with accuracies very close to the exact solutions.and ∂ α u(x,t) ∂t α denote the Caputo fractional derivative of order 2α and α, respectively, which will be defined in Sect. 2.This model has been developed to overcome the shortcomings of the classical telegraph equation which might not adequately model the abnormal diffusion phenomena during a long transmission process in a transmission line [2].

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“…Aronszajn has given a systematic reproducing kernel theory containing the Bergman kernel function [10]. For more details, see [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

New Numerical Method for Solving Tenth Order Boundary Value Problems

Akgül

Băleanu

et al. 2018

Mathematics

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In this paper, we implement reproducing kernel Hilbert space method to tenth order boundary value problems. These problems are important for mathematicians. Different techniques were applied to get approximate solutions of such problems. We obtain some useful reproducing kernel functions to get approximate solutions. We obtain very efficient results by this method. We show our numerical results by tables.

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Using reproducing kernel for solving a class of time-fractional telegraph equation with initial value conditions

Cited by 12 publications

References 23 publications

A novel numerical implementation for solving time fractional telegraph differential equations having multiple space and time delays via Delannoy polynomial

A novel numerical implementation for solving time fractional telegraph differential equations having multiple space and time delays via Delannoy polynomial

Extended cubic B-splines in the numerical solution of time fractional telegraph equation

New Numerical Method for Solving Tenth Order Boundary Value Problems

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