scholarly journals Extensions to common Laplace and Fourier transforms

1997 ◽  
Vol 4 (11) ◽  
pp. 310-312 ◽  
Author(s):  
L. Onural ◽  
M.F. Erden ◽  
H.M. Ozaktas
Keyword(s):  
Fourier Transforms ◽  
Laplace And Fourier Transforms

scholarly journals Response Due To Impulsive Force In Generalized Thermomicrostretch Elastic Solid

2015 ◽  
Vol 20 (3) ◽  
pp. 487-502
Author(s):  
V. Kumar ◽  
R. Singh
Keyword(s):  
Fourier Transforms ◽  
Normal Force ◽  
Elastic Solid ◽  
Integral Transforms ◽  
Normal Displacement ◽  
Impulsive Force ◽  
Field Equations ◽  
Laplace And Fourier Transforms ◽  
Eigen Value ◽  
Plain Strain

Abstract A two dimensional Cartesian model of a generalized thermo-microstretch elastic solid subjected to impulsive force has been studied. The eigen value approach is employed after applying the Laplace and Fourier transforms on the field equations for L-S and G-L model of the plain strain problem. The integral transforms have been inverted into physical domain numerically and components of normal displacement, normal force stress, couple stress and microstress have been illustrated graphically.

scholarly journals Solutions of Unified Fractional Schrödinger Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
V. B. L. Chaurasia ◽  
Devendra Kumar
Keyword(s):  
Schrödinger Equation ◽  
Closed Form ◽  
Numerical Computation ◽  
Schrodinger Equation ◽  
Fourier Transforms ◽  
Schrödinger Equations ◽  
Laplace And Fourier Transforms ◽  
Fractional Schrödinger Equation ◽  
Fractional Schrödinger Equations ◽  
Fractional Schrodinger Equation

We obtain the solution of a unified fractional Schrödinger equation. The solution is derived by the application of the Laplace and Fourier transforms in closed form in terms of the Mittag-Leffler function. The result obtained here is quite general in nature and capable of yielding a very large number of results (new and known) hitherto scattered in the literature. Most of results obtained are in a form suitable for numerical computation.

Generalized GL Fractional Derivative and Its Laplace and Fourier Transform

2009 ◽  
Author(s):  
Manuel D. Ortigueira ◽  
Juan J. Trujillo
Keyword(s):  
Fourier Transform ◽  
Linear System ◽  
Fractional Derivative ◽  
Frequency Response ◽  
Fourier Transforms ◽  
Laplace And Fourier Transforms ◽  
Riesz Fractional Derivative ◽  
Laplace And Fourier Transform

It is well known the difficulties that the Riesz fractional derivative present, as the spatial fractional derivative involved in many models of the dynamics of anomalous processes. The generalized Gru¨nwal-Letnikov fractional derivative is analysed in this paper. Its Laplace and Fourier Transforms are computed and some current results criticized. It is shown that only the forward derivative of a sinusoid exists. This result is used to define the frequency response of a fractional linear system.

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.

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