• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.695-703
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• 2002

The fractional order evolutionary integral equations have been considered by first author in [6], the existence, uniqueness and some other properties of the solution have been proved. Here we study the continuation of the solution and its fractional order derivative. Also we study the generality of this problem and prove that the fractional order diffusion problem, the fractional order wave problem and the initial value problem of the equation of evolution are special cases of it. The abstract diffusion-wave problem will be given also as an application.

• Wind and Structures
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• 제35권6호
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• pp.395-403
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• 2022

The present research is concerned with the study of Stoneley wave propagation at the interface of two dissimilar homogeneous orthotropic magneto-thermoelastic solids with fractional order theory of type GN-III with three phase-lags and combined effect of hall current and rotation. With the help of appropriate boundary conditions the secular equations of Stoneley waves are obtained in the form of determinant. The characteristics of wave such as phase velocity, attenuation coefficient and specific loss are computed numerically. The effect of rotation on the Stoneley wave's phase velocity, attenuation coefficient, specific loss, displacement components, stress components and temperature change has been depicted graphically. Some particular cases are also derived in this problem.

• Structural Engineering and Mechanics
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• 제68권2호
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• pp.215-226
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• 2018

In this article, the theory of fractional order two temperature generalized thermoelasticity is employed to study the wave propagation in a fiber reinforced anisotropic thermoelastic half space in the presence of moving internal heat source. The whole space is assumed to be under the influence of gravity. The surface of the half-space is subjected to an inclined load. Laplace and Fourier transform techniques are employed to solve the problem. Expressions for different field variables in the physical domain are derived by the application of numerical inversion technique. Physical fields are presented graphically to study the effects of gravity and heat source. Effects of time, reinforcement, fractional parameter and inclination of load have also been reported. Results of some earlier workers have been deduced from the present analysis.

• Advances in materials Research
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• 제12권3호
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• pp.211-226
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• 2023

The present work is considered to study the two-dimensional problem in an orthotropic magneto-thermoelastic media and examined the effect of thermal phase-lags and GN-theories on Rayleigh waves in the light of fractional order theory with combined effect of rotation and hall current. The boundary conditions are used to derive the secular equations of Rayleigh waves. The wave properties such as phase velocity, attenuation coefficient are computed numerically. The numerical simulated results are presented graphically to show the effect of phase-lags and GN-theories on the Rayleigh wave phase velocity, attenuation coefficient, stress components and temperature change. Some particular cases are also discussed in the present investigation.

• 대한수학회지
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• 제53권4호
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• pp.929-967
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• 2016

Let p(t, x) be the fundamental solution to the problem $${\partial}^{\alpha}_tu=-(-{\Delta})^{\beta}u,\;{\alpha}{\in}(0,2),\;{\beta}{\in}(0,{\infty})$$. If ${\alpha},{\beta}{\in}(0,1)$, then the kernel p(t, x) becomes the transition density of a Levy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t, x) and its space and time fractional derivatives $$D^n_x(-{\Delta}_x)^{\gamma}D^{\sigma}_tI^{\delta}_tp(t,x),\;{\forall}n{\in}{\mathbb{Z}}_+,\;{\gamma}{\in}[0,{\beta}],\;{\sigma},{\delta}{\in}[0,{\infty})$$, where $D^n_x$ x is a partial derivative of order n with respect to x, $(-{\Delta}_x)^{\gamma}$ is a fractional Laplace operator and $D^{\sigma}_t$ and $I^{\delta}_t$ are Riemann-Liouville fractional derivative and integral respectively.

• 대한기계학회논문집B
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• 제24권12호
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• pp.1555-1569
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• 2000

Numerical simulation of fluid flow with moving free surface has been carried out. For the free surface flow, a VOF(Volume of Fluid)-based algorithm utilizing a fixed grid system has been investigated. In order to reduce numerical smearing at the free surface represented on a fixed grid system, a new free surface tracking algorithm based on the donor-acceptor scheme has been presented. Novel features of the proposed algorithm are characterized as two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby-cell to determine the fluid volume flux at each cell boundary. The proposed algorithm can be easily implemented in any irregular non-uniform grid systems that are usual in finite element method (FEM). Moreover, the proposed algorithm can be extended and applied to the 3-D free surface flow problem without additional efforts. For computation of unsteady incompressible flow, a finite element approximation based on the explicit fractional step method has been adopted. In addition, the SUPG(streamline upwind/Petrov-Galerkin) method has been implemented to deal with convection dominated flows. Combination of the proposed free surface tracking scheme and explicit fractional step formulation resulted in an efficient solution algorithm. Validity of the present solution algorithm was demonstrated from its application to the broken dam and the solitary wave propagation problems.

• 대한토목학회논문집
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• 제28권5B호
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• pp.575-589
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• 2008

본 연구는 지진해일단파(tsunami bore) 혹은 조석단파(tidal bore)와 같은 단파의 동수역학적인 거동특성을 검토할 목적으로, 댐파괴류에서 단파의 형성과 동일한 방법, 즉 수조의 한쪽 끝단에 있는 고수위의 저수조(貯水槽) 게이트를 순간적으로 제거하는 방법으로 단파를 발생시킨다. 이러한 단파의 형성과 전파에 관한 수치시뮬레이션에 이상유(二相流)모델에 기초한 Navier-Stokes식을 적용하며, 이 때 비압축성 및 비혼합성의 액체와 기체흐름을 각각 고려한다. 기체와 액체의 접면을 VOF법으로 추적하고, Navier-Stokes방정식을 수치적으로 풀기 위하여 MCIP법을 적용한다. 1차원인 CIP법을 분할스텝기법을 사용하여 고차원으로 확장한 MCIP법은 수치확산이 매우 작고, 또한 안정된 스킴으로 알려져 있다. 게다가, 난류를 시뮬레이션하기 위하여 그의 유용성이 잘 알려져 있는 LES모델을 사용한다. 단파의 형성과 전파에 관한 수치해석결과를 검증하기 위하여 수리실험을 수행하였으며, 시간경과에 따른 수위변동과 평균유속변동에 대한 수치해석결과 및 실험결과를 비교하여 매우 양호한 상호대응관계를 확인할 수 있었다.