• Title, Summary, Keyword: Fourier(-Laplace) transform

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EXACT SOLUTIONS OF GENERALIZED STOKES' PROBLEMS FOR AN INCOMPRESSIBLE COUPLE STRESS FLUID FLOWS

  • SIDDIQUE, IMRAN;UMBREEN, YOUSRA
    • Journal of applied mathematics & informatics
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    • v.37 no.5_6
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    • pp.507-519
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    • 2019
  • The ground for this paper is to examine the generalized Stokes' first and second issues for an incompressible couple pressure liquid under isothermal conditions. Exact solutions for each problem are acquired by using the Laplace transform (LT) with respect to the time variable t and the sine Fourier transform (FT) with respect to the y-variable. Further, a comparison is given of the obtained results and the results of Devakar and Lyengar [1] and by using the four inverse Laplace transform algorithms (Stehfest's, Tzou's, Talbot, Fourier series) in the space time domain utilizing a numerical methodology. Moreover, velocity profiles are plotted and considered for various occasions and distinctive estimations of couple stress parameters. At the end, the outcomes are exhibited by graphs and in tabular forms.

CERTAIN RESULTS INVOLVING FRACTIONAL OPERATORS AND SPECIAL FUNCTIONS

  • Aghili, Arman
    • Korean Journal of Mathematics
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    • v.27 no.2
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    • pp.487-503
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    • 2019
  • In this study, the author provided a discussion on one dimensional Laplace and Fourier transforms with their applications. It is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve space fractional partial differential equation with non - constant coefficients. The object of the present article is to extend the application of the joint Fourier - Laplace transform to derive an analytical solution for a variety of time fractional non - homogeneous KdV. Numerous exercises and examples presented throughout the paper.

Numerical Inversion Technique for the One and Two-Dimensional L2-Transform Using the Fourier Series and Its Application to Fractional Partial Differential Equations

  • Aghili, Arman;Ansari, Alireza
    • Kyungpook Mathematical Journal
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    • v.52 no.4
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    • pp.383-395
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    • 2012
  • In this paper, we use a computational algorithm for the inversion of the one and two-dimensional $\mathcal{L}_2$-transform based on the Bromwich's integral and the Fourier series. The new inversion formula can evaluate the inverse of the $\mathcal{L}_2$-transform with considerable accuracy over a wide range of values of the independent variable and can be devised for the functions which are not Laplace transformable and have damping motion in small interval near origin.

Thermomechanical interactions in transversely isotropic magneto thermoelastic solid with two temperatures and without energy dissipation

  • Lata, Parveen;Kaur, Iqbal
    • Steel and Composite Structures
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    • v.32 no.6
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    • pp.779-793
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    • 2019
  • The purpose of this research paper is to depict the thermomechanical interactions in transversely isotropic magneto thermoelastic solid with two temperatures and without energy dissipation in generalized LS theories of thermoelasticity. The Laplace and Fourier transform techniques have been used to find the solution of the problem. The displacement components, stress components, and conductive temperature distribution with the horizontal distance are computed in the transformed domain and further calculated in the physical domain numerically. The effect of two temperature and relaxation time are depicted graphically on the resulting quantities.

DENSENESS OF TEST FUNCTIONS IN THE SPACE OF EXTENDED FOURIER HYPERFUNCTIONS

  • Kim, Kwang-Whoi
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.4
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    • pp.785-803
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    • 2004
  • We research properties of analytic functions which are exponentially decreasing or increasing. Also we show that the space of test functions is dense in the space of extended Fourier hyper-functions, and that the Fourier transform of the space of extended Fourier hyperfunctions into itself is an isomorphism and Parseval's inequality holds.

Fourier Series Approximation for the Generalized Baumgartner Statistic

  • Ha, Hyung-Tae
    • Communications for Statistical Applications and Methods
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    • v.19 no.3
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    • pp.451-457
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    • 2012
  • Baumgartner et al. (1998) proposed a novel statistical test for the null hypothesis that two independently drawn samples of data originate from the same population, and Murakami (2006) generalized the test statistic for more than two samples. Whereas the expressions of the exact density and distribution functions of the generalized Baumgartner statistic are not yet found, the characteristic function of its limiting distribution has been obtained. Due to the development of computational power, the Fourier series approximation can be readily utilized to accurately and efficiently approximate its density function based on its Laplace transform. Numerical examples show that the Fourier series method provides an accurate approximation for statistical quantities of the generalized Baumgartner statistic.

Fractional order generalized thermoelastic study in orthotropic medium of type GN-III

  • Lata, Parveen;Zakhmi, Himanshi
    • Geomechanics and Engineering
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    • v.19 no.4
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    • pp.295-305
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    • 2019
  • The present paper is concerned with the investigation of disturbances in orthotropic thermoelastic medium by using fractional order heat conduction equation with three phase lags due to thermomechanical sources. Laplace and Fourier transform techniques are used to solve the problem. The expressions for displacement components, stress components and temperature change are derived in transformed domain and further in physical domain using numerical inversion techniques. The effect of fractional parameter based on its conductivity i.e., ($0<{\alpha}<1$ for weak, ${\alpha}=1$ for normal, $1<{\alpha}{\leq}2$ for strong conductivity) is depicted graphically on various components.

Effects of Hall current in a transversely isotropic magnetothermoelastic with and without energy dissipation due to normal force

  • Kumar, Rajneesh;Sharma, Nidhi;Lata, Parveen
    • Structural Engineering and Mechanics
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    • v.57 no.1
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    • pp.91-103
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    • 2016
  • This investigation is concerned with the disturbances in a homogeneous transversely isotropic thermoelastic rotating medium with two temperature, in the presence of the combined effects of Hall currents and magnetic field due to normal force of ramp type. The formulation is applied to the thermoelasticity theories developed by Green-Naghdi Theories of Type-II and Type-III. Laplace and Fourier transform technique is applied to solve the problem. The analytical expressions of displacements, stress components, temperature change and current density components are obtained in the transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically to show the effects of Hall current and anisotropy on the resulting quantities. Some special cases are also deduced from the present investigation.

Integral Transforms in Electromagnetic Formulation

  • Eom, Hyo Joon
    • Journal of electromagnetic engineering and science
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    • v.14 no.3
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    • pp.273-277
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    • 2014
  • In this research, integral transform technique for electromagnetic scattering formulation is reviewed. Electromagnetic boundary-value problems are presented to demonstrate how the integral transforms are utilized in electromagnetic propagation, antennas, and electromagnetic interference/compatibility. Various canonical structures of slotted conductors are used for illustration; moreover, Fourier transform, Hankel transform, Mellin transform, Kontorovich-Lebedev transform, and Weber transform are presented. Starting from each integral transform definition, the general procedures for solving Helmholtz's equation or Laplace's equation for the potentials in the unbounded region are reviewed. The boundary conditions of field continuity are incorporated into particular formulations. Salient features of each integral transform technique are discussed.