• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.339-350
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• 2005

A space-time fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order $\alpha{\in}(0,1]$, and the second-order space derivative is replaced with a Riesz-Feller derivative of order $\beta{\in}0,2]$. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-dispersion equation whose space and time derivatives both replacing with Caputo derivatives.

• 한국통신학회논문지
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• 제14권4호
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• pp.360-368
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• 1989

본 논문에서는 cut-through 스위칭 방식으로 음성과 데이터를 집적하였을때, 그 성능을 분석하고 패켓 스위칭 방식과 비교하였다. 우선 음성과 데이터 패켓이 네트웍 내의 한 node를 cut-through할 확률을 유도하고, 각각의 네트웍 delay의 Laplace transform을 구했다. 분석결과로 부터 cut-through 스위칭 방식이 패켓 스위칭 방식보다 성능이 우수함을 알 수 있다.

• Smart Structures and Systems
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• 제21권2호
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• pp.163-170
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• 2018

The dynamic response of a finite length thermo-piezoelectric rod with variable material properties is investigated in the context of the fractional order theory of thermoelasticity. The rod is subjected to a moving heat source and fixed at both ends. The governing equations are formulated and then solved by means of Laplace transform together with its numerical inversion. The results of the non-dimensional temperature, displacement and stress in the rod are obtained and illustrated graphically. Meanwhile, the effects of the fractional order parameter, the velocity of heat source and the variable material properties on the variations of the considered variables are presented, and the results show that they significantly influence the variations of the considered variables.

• Structural Engineering and Mechanics
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• 제23권2호
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• pp.163-175
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• 2006

In this paper, the dynamic response of a piezoelectric layer with a penny-shaped crack is investigated. The piezoelectric layer is subjected to an axisymmetrical action of both mechanical and electrical impacts. Two kinds of crack surface conditions, i.e., electrically impermeable and electrically permeable, are adopted. Based upon integral transform technique, the crack boundary value problem is reduced to a system of Fredholm integral equations in the Laplace transform domain. By making use of numerical Laplace inversion the time-dependent dynamic stress and electric displacement intensity factors are obtained, and the dynamic energy release rate is further derived. Numerical results are plotted to show the effects of both the piezoelectric layer thickness and the electrical impact loadings on the dynamic fracture behaviors of the crack tips.

• 대한수학회논문집
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• 제31권4호
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• pp.779-790
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• 2016

Using the extended generalized integral transform given by Luo et al. [6], we introduce some new generalized integral transforms to investigate such their (potentially) useful properties as inversion formulas and Parseval-Goldstein type relations. Classical integral transforms including (for example) Laplace, Stieltjes, and Widder-Potential transforms are seen to follow as special cases of the newly-introduced integral transforms.

• International Journal of Reliability and Applications
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• 제16권1호
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• pp.27-34
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• 2015

Based on increasing concave ordering a new class of life distribution is introduced. The new class of life distribution is named used better than aged in increasing concave ordering and is denoted by UBAC(2). The implication of our proposed class of life distribution with other classes is given. The properties of UBAC(2) under convolution, discrete mixture and formation of a coherent system are studied. Finally a characterization of the proposed class of life distributions by Laplace transform is discussed.

• Structural Engineering and Mechanics
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• 제69권6호
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• pp.607-614
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• 2019

The present investigation has focus on the study of deformation due to thermomechanical sources in a thick circular plate. The thick circular plate is homogeneous, transversely isotropic with two temperatures and without energy dissipation. The upper and lower surfaces of the thick circular plate are traction free. The Laplace and Hankel transform has been used for finding the general solution to the field equations. The analytical expressions of stresses, conductive temperature and displacement components are computed in the transformed domain. However, the resulting quantities are obtained in the physical domain by using numerical inversion technique. Numerically simulated results are illustrated graphically. The effects of two temperatures by considering different values of temperature parameters are shown on the various components. Some particular cases are also figured out from the present investigation.

• Korean Chemical Engineering Research
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• 제57권5호
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• pp.652-665
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• 2019

Analytical solutions of the reactant concentration inside porous spherical catalytic particles were obtained from unsteady reaction-diffusion equation by applying eigenfunction expansion method. Various surface concentrations as exponentially decaying or oscillating function were considered as boundary conditions to solve the unsteady partial differential equation as a function of radial distance and time. Dirac delta function was also used for the instantaneous injection of the reactant as the surface boundary condition to calculate average reactant concentration inside the particles as a function of time by Laplace transform. Besides spherical morphology, other geometries of particles, such as cylinder or slab, were considered to obtain the solution of the reaction-diffusion equation, and the results were compared with the solution in spherical coordinate. The concentration inside the particles based on calculation was compared with the bulk concentration of the reactant molecules measured by photocatalytic decomposition as a function of time.

• Structural Engineering and Mechanics
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• 제70권2호
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• pp.245-255
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• 2019

In present research, we have considered transversely isotropic magneto thermoelastic solid with two temperature and without energy dissipation due to inclined load. The mathematical model has been formulated using Lord-Shulman theory. The Laplace and Fourier transform techniques have been used to find the solution to 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 using numerical inversion techniques. The effect of rotation and angle of inclination of inclined load is depicted graphically on the resulting quantities.

• Advances in materials Research
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• 제7권3호
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• pp.203-220
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• 2018

This investigation is focused on the study of effect of hall current in transversely isotropic magneto thermoelastic homogeneous medium with fractional order heat transfer and rotation. As an application the bounding surface is subjected to normal force. The research becomes more interesting due to interaction of Hall current with the effect of rotation as it has found various applications. Laplace and Fourier transform is used for solving field equations. The analytical expressions of temperature, displacement components, stress components and current density components are computed in the transformed domain. The effects of hall current and fractional order parameter at different values are represented graphically.