Analysis of Solutions of Time Fractional Telegraph Equation

Nirmala, R. Joice; Balachandran, K.

doi:10.12941/jksiam.2014.18.209

Cited by 8 publications

(4 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…a nonhomogeneous time fractional telegraph equation in [25]. Taking single Laplace transform to initial (45) and boundary conditions (46), we get 1 ( ) = 2 ( ) = 0,…”

Section: International Journal Of Mathematics and Mathematical Sciencesmentioning

confidence: 99%

Double Laplace Transform Method for Solving Space and Time Fractional Telegraph Equations

Dhunde

Waghmare²

2016

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

show abstract

“…a nonhomogeneous time fractional telegraph equation in [25]. Taking single Laplace transform to initial (45) and boundary conditions (46), we get 1 ( ) = 2 ( ) = 0,…”

Section: International Journal Of Mathematics and Mathematical Sciencesmentioning

confidence: 99%

Double Laplace Transform Method for Solving Space and Time Fractional Telegraph Equations

Dhunde

Waghmare²

2016

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

show abstract

“…Orsingher and Zhao [10] demonstrated that TFTEs determine the telegraph processes with Brownian time and the law of iterated Brownian motion. Apart from that, Nirmala and Balachandran [11] studied the application of the TFTEs to calculate signal and power losses during transmission media in a communication system. Furthermore, Vyawahare and Nataraj [12] modelled a neutron transport in a nuclear reactor using the TFTE.…”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Solution for Time-Fractional Nonlinear Telegraph Equations with Source Term

Abdul Rahman Farhan Sabdin,

Che Haziqah Che Hussin,

Graygorry Brayone Ekal

et al. 2023

ARASET

View full text Add to dashboard Cite

In this study, we considered time-fractional nonlinear telegraph equations (TFNLTEs). For solving the TFNLTEs, we deployed a method known as the Multistep Modified Reduced Differential Transform Method (MMRDTM). Prior to the multistep technique, the nonlinear term in TFNLTEs is replaced with corresponding Adomian polynomials. It can be observed that the MMRDTM is much simpler and more straightforward. On top of that, it works exceptionally where the obtained solutions are more accurately approximated over time. To demonstrate the performance of the MMRDTM in terms of its capabilities and accuracies, we provided two numerical examples of solving TFNLTEs by using MMRDTM and Modified Reduced Differential Transform Method (MRDTM). By comparing the absolute errors of the obtained solutions by both methods, we demonstrated that the solutions provided by the MMRDTM much closer to the exact solutions compared to the corresponding solutions yielded by the MRDTM. This justified that the MMRDTM provides highly accurate and precise solutions for the TFNLTEs.

show abstract

“…The telegraph equation is a hyperbolic PDE that has many applications in physics and engineering, for example, in signal analysis, random walk theory, anomalous diffusion processes, wave phenomena, and wave propagation of the electrical signal in the cable of a transmission line. Different numerical and analytical techniques have been used to solve fractional-order telegraph equations [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

A Semi-Discretization Method Based on Finite Difference and Differential Transform Methods to Solve the Time-Fractional Telegraph Equation

Sahraee,

Arabameri

2023

Symmetry

View full text Add to dashboard Cite

The telegraph equation is a hyperbolic partial differential equation that has many applications in symmetric and asymmetric problems. In this paper, the solution of the time-fractional telegraph equation is obtained using a hybrid method. The numerical simulation is performed based on a combination of the finite difference and differential transform methods, such that at first, the equation is semi-discretized along the spatial ordinate, and then the resulting system of ordinary differential equations is solved using the fractional differential transform method. This hybrid technique is tested for some prominent linear and nonlinear examples. It is very simple and has a very small computation time; also, the obtained results demonstrate that the exact solutions are exactly symmetric with approximate solutions. The results of our scheme are compared with the two-dimensional differential transform method. The numerical results show that the proposed method is more accurate and effective than the two-dimensional fractional differential transform technique. Also, the implementation process of this method is very simple, so its computer programming is very fast.

show abstract

Analysis of Solutions of Time Fractional Telegraph Equation

Cited by 8 publications

References 31 publications

Double Laplace Transform Method for Solving Space and Time Fractional Telegraph Equations

Double Laplace Transform Method for Solving Space and Time Fractional Telegraph Equations

Approximate Analytical Solution for Time-Fractional Nonlinear Telegraph Equations with Source Term

A Semi-Discretization Method Based on Finite Difference and Differential Transform Methods to Solve the Time-Fractional Telegraph Equation

Contact Info

Product

Resources

About