An approximate analytical solution of time-fractional telegraph equation

Das, S.; Vishal, K.; Gupta, Praveen Kumar; Yıldırım, Ahmet

doi:10.1016/j.amc.2011.02.030

Cited by 42 publications

(23 citation statements)

References 19 publications

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“…Similarly, the three dimensional (3D) telegraphic equation 69 is expressed as follows: uðx; y; z; tÞ ¼ n 1 ðx; y; z; tÞ; ðx; y; zÞ 2 C p ; t P 0; @u @g ðx; y; z; 0Þ ¼ n 2 ðx; y; z; tÞ; ðx; y; zÞ 2 C q ; t P 0; iðx; y; z; tÞ ¼ w 1 ðx; y; z; tÞ; ðx; y; zÞ 2 C p ; t P 0; @i @g ðx; y; z; 0Þ ¼ w 2 ðx; y; z; tÞ; ðx; y; zÞ 2 C q ; t P 0; wave propagation (Weston and He, 1993), random walk theory 93 (Banasiak and Mika, 1998) Das et al, 2011;Srivastava et al, 2013a,b;Ahmad and 103 Hassan, 2013; Keskin and Oturanc, 2009). 104 The present paper describes an analytical scheme, the 105 reduced differential transform method to provide approximate wðx; y; z; tÞ ¼ X 1 …”

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confidence: 99%

Reduced differential transform method to solve two and three dimensional second order hyperbolic telegraph equations

Srivastava

Awasthi

Chaurasia

2017

Journal of King Saud University - Engineering Sciences

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Reduced differential transform method to solve 5 two and three dimensional second order hyperbolic 6 telegraphic equations Q1 7 Abstract In this article, an analytical solution procedure is described for solving two and three dimensional second order hyperbolic telegraph equation Q3 using a reliable semi-analytic method so called the reduced differential transform method (RDTM) subject to the appropriate initial condition. Using this method, it is possible to find an exact solution or a closed approximate solution of a differential equation. Various numerical examples are carried out to check the accuracy, efficiency, and convergence of the described method. The method is a powerful mathematical tool for solving a wide range of problems arising in engineering and sciences.

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mentioning

confidence: 99%

Reduced differential transform method to solve two and three dimensional second order hyperbolic telegraph equations

Srivastava

Awasthi

Chaurasia

2017

Journal of King Saud University - Engineering Sciences

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“…Also, Huang derived the solution for the bounded problem in a bounded-space domain by means of Sine-Laplace transforms methods. Das et al [14] used a homotopy analysis method in approximating an analytical solution for the time-fractional telegraph equation and different particular cases have been derived. Jiang and Lin [15] obtained the solution in a series form for the time-fractional telegraph equation with Robin boundary value conditions using the reproducing kernel theorem.…”

Section: Introductionmentioning

confidence: 99%

A New Technique of Laplace Variational Iteration Method for Solving Space-Time Fractional Telegraph Equations

Alawad

Yousif

Arbab

2013

International Journal of Differential Equations

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In this paper, the exact solutions of space-time fractional telegraph equations are given in terms of Mittage-Leffler functions via a combination of Laplace transform and variational iteration method. New techniques are used to overcome the difficulties arising in identifying the general Lagrange multiplier. As a special case, the obtained solutions reduce to the solutions of standard telegraph equations of the integer orders.

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“…Fino et al [29] presented the solution of space-and time-fractional telegraph equations with a fractional Laplacian operator in terms of multi-variate Mittag-Leffler type functions. Das et al [30] applied an homotopy analysis to study the explicit solutions of a time-fractional telegraph equation. Povestenko [31] obtained the fundamental solution to the nonhomogeneous space-time-fractional telegraph equation as well as the corresponding thermal stresses in the axisymmetric case.…”

Section: Introductionmentioning

confidence: 99%

“…Many authors have studied the properties of the fractional telegraph equation (see [19][20][21][22][23][27][28][29][30][31][32][33][34]). Ortigueira [19,20] considered time-and space-fractional telegraph equations and related fractional telegraph processes.…”

Section: Introductionmentioning

confidence: 99%

High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

Chen

Jiang

Liu

et al. 2015

Journal of Computational and Applied Mathematics

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a b s t r a c tIn this paper, a class of unconditionally stable difference schemes based on the Padé approximation is presented for the Riesz space-fractional telegraph equation. Firstly, we introduce a new variable to transform the original differential equation to an equivalent differential equation system. Then, we apply a second order fractional central difference scheme to discretize the Riesz space-fractional operator. Finally, we use (1, 1), (2, 2) and (3, 3) Padé approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations. Matrix analysis is used to show the unconditional stability of the proposed algorithms. Two examples with known exact solutions are chosen to assess the proposed difference schemes. Numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space-fractional hyperbolic equation.

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An approximate analytical solution of time-fractional telegraph equation

Cited by 42 publications

References 19 publications

Reduced differential transform method to solve two and three dimensional second order hyperbolic telegraph equations

Reduced differential transform method to solve two and three dimensional second order hyperbolic telegraph equations

A New Technique of Laplace Variational Iteration Method for Solving Space-Time Fractional Telegraph Equations

High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

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