scholarly journals Analytical Solution for the Time-Fractional Telegraph Equation

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
F. Huang
Keyword(s):  
Analytical Solution ◽  
Laplace Transform ◽  
Boundary Problem ◽  
Fourier Transforms ◽  
Telegraph Equation ◽  
Green Functions ◽  
Laplace And Fourier Transforms ◽  
Sine Transform ◽  
Fractional Telegraph Equation ◽  
Bounded Space

We discuss and derive the analytical solution for three basic problems of the so-called time-fractional telegraph equation. The Cauchy and Signaling problems are solved by means of juxtaposition of transforms of the Laplace and Fourier transforms in variabletandx,respectively. the appropriate structures and negative prosperities for their Green functions are provided. The boundary problem in a bounded space domain is also solved by the spatial Sine transform and temporal Laplace transform, whose solution is given in the form of a series.

scholarly journals A non-differentiable solution for the local fractional telegraph equation

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 225-231
Author(s):  
Jie Li ◽  
Ce Zhang ◽  
Weixing Liu ◽  
Yuzhu Zhang ◽  
Aimin Yang ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Fractional Derivative ◽  
Series Expansion ◽  
Expansion Method ◽  
Telegraph Equation ◽  
Differentiable Solution ◽  
Local Fractional Derivative ◽  
Fractional Telegraph Equation ◽  
Telegraph Equations ◽  
Series Expansion Method

In this paper, we consider the linear telegraph equations with local fractional derivative. The local fractional Laplace series expansion method is used to handle the local fractional telegraph equation. The analytical solution with the non-differentiable graphs is discussed in detail. The proposed method is efficient and accurate.

scholarly journals Doppler effect described by the solutions of the Cattaneo telegraph equation

2020 ◽  
Author(s):  
Yuriy Povstenko ◽  
Martin Ostoja-Starzewski
Keyword(s):  
Doppler Effect ◽  
Heat Conduction Equation ◽  
Fourier Transforms ◽  
Telegraph Equation ◽  
Laplace And Fourier Transforms ◽  
Wave Fronts ◽  
Time Harmonic ◽  
The Doppler Effect ◽  
Harmonic Source ◽  
Steady State Solutions

AbstractThe Cattaneo telegraph equation for temperature with moving time-harmonic source is studied on the line and the half-line domain. The Laplace and Fourier transforms are used. Expressions which show the wave fronts and elucidate the Doppler effect are obtained. Several particular cases of the considered problem including the heat conduction equation and the wave equation are investigated. The quasi-steady-state solutions are also examined for the case of non-moving time-harmonic source and time-harmonic boundary condition for temperature.

Analytical method for space-fractional telegraph equation by homotopy perturbation transform method

2016 ◽  
Vol 5 (2) ◽  
Author(s):  
Amit Prakash
Keyword(s):  
Laplace Transform ◽  
Present Article ◽  
Analytical Method ◽  
Telegraph Equation ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Fractional Telegraph Equation

AbstractThe object of the present article is to study spacefractional telegraph equation by fractional Homotopy perturbation transform method (FHPTM). The homotopy perturbation transform method is an innovative adjustment in Laplace transform algorithm. Three test examples are presented to show the efficiency of the proposed technique.

RADIATION FROM A FINITE CYLINDRICAL EXPLOSIVE SOURCE

Geophysics ◽  
1977 ◽  
Vol 42 (7) ◽  
pp. 1384-1393 ◽  
Author(s):  
Anas M. Abo‐Zena
Keyword(s):  
Fourier Transform ◽  
Laplace Transform ◽  
Fourier Transforms ◽  
Inverse Fourier Transform ◽  
Applied Pressure ◽  
Inverse Laplace Transform ◽  
Laplace And Fourier Transforms ◽  
Explosion Pressure ◽  
Explosive Source ◽  
The Laplace Transform

For an elastic material with an infinite circular cylindrical hole, the exact solution due to a pressure on a finite length of the cylinder is obtained as a function of the Laplace transform parameter on time and Fourier transform parameter on the z-coordinate (the axis of the cylinder). The applied pressure is a function of the time and the position z. Numerical inversion of the Laplace and Fourier transforms are required to determine the field quantities in the time and space parameters. In the far field, the inverse Fourier transform can be obtained by an asymptotic expansion. It remains to obtain the inverse Laplace transform numerically. We have found that for cylinders whose radius is small compared with the smallest wavelength of interest, an analytical solution can be obtained. Graphical results for the cases of instantaneous explosion and progression of the detonation with constant velocity are given. In both cases an exponential decay of the explosion pressure is assumed.

scholarly journals Analytical solutions of some general classes of differential and integral equations by using the Laplace and Fourier transforms

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 2869-2876
Author(s):  
H.M. Srivastava ◽  
Mohammad Masjed-Jamei ◽  
Rabia Aktaş
Keyword(s):  
Fourier Transform ◽  
Laplace Transform ◽  
Integral Equations ◽  
Analytical Solutions ◽  
General Class ◽  
Fourier Transforms ◽  
Laplace And Fourier Transforms ◽  
The Laplace Transform ◽  
The Fourier Transform ◽  
Differential And Integral Equations

This article deals with a general class of differential equations and two general classes of integral equations. By using the Laplace transform and the Fourier transform, analytical solutions are derived for each of these classes of differential and integral equations. Some illustrative examples and particular cases are also considered. The various analytical solutions presented in this article are potentially useful in solving the corresponding simpler differential and integral equations.

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