• Geomechanics and Engineering
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• 제21권1호
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• pp.85-93
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• 2020

In this article, the generalized thermoelastic theory with fractional derivative is presented to estimate the variation of temperature, the components of stress, the components of displacement and the changes in volume fraction field in two-dimensional porous media. Easily, the exact solutions in the Laplace domain are obtained. By using Laplace and Fourier transformations with the eigenvalues method, the physical quantities are obtained analytically. The numerical results for all the physical quantities considered are implemented and presented graphically. The results display that the present model with the fractional derivative is reduced to the Lord and Shulman (LS) and the classical dynamical coupled (CT) theories when the fractional parameter is equivalent to one and the delay time is equal to zero and respectively.

• Journal of the Korean Data and Information Science Society
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• 제16권3호
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• pp.539-547
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• 2005

We propose the Bayesian testing for the equality of two independent Inverse Gaussian population means using the fractional Bayesian factors suggested by O' Hagan(1995). As prior distribution for the parameters, we assumed the noninformative priors. In order to investigate the usefulness of the proposed Bayesian testing procedures, the behaviors of the proposed results are examined via real data analysis.

• Journal of applied mathematics & informatics
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• 제36권1_2호
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• pp.107-114
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• 2018

We establish some new ostrowski type inequalities for MT-convex function including first order derivative via Niemann-Trouvaille fractional integral. It is interesting to mention that our results provide new estimates on these types of integral inequalities for MT-convex functions.

• 대한수학회논문집
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• 제37권4호
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• pp.1099-1129
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• 2022

In this paper, we establish Liouville type theorems for the fractional powers of multidimensional Bessel operators extending the results given in [6]. In order to do this, we consider the distributional point of view of fractional Bessel operators studied in [12].

• 대한수학회논문집
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• 제38권1호
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• pp.281-298
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• 2023

A class of systems of Caputo fractional differential equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a uniform mesh is proposed. Supremum norm is used to derive an error estimate which is of order κ − 1, 1 < κ < 2. Numerical examples are given which validate our theoretical results.

• Journal of Power Electronics
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• 제19권4호
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• pp.835-845
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• 2019

This paper presents a robust-optimal control strategy to improve the output-voltage error-tracking and control capability of a DC-DC boost converter. The proposed strategy employs an optimized Fractional-order Proportional-Integral (FoPI) controller that serves to eliminate oscillations, overshoots, undershoots and steady-state fluctuations. In order to significantly improve the error convergence-rate during a transient response, the FoPI controller is augmented with a pre-stage nonlinear error-modulator. The modulator combines the variations in the error and error-derivative via the signed-distance method. Then it feeds the aggregated-signal to a smooth sigmoidal control surface constituting an optimized hyperbolic secant function. The error-derivative is evaluated by measuring the output-capacitor current in order to compensate the hysteresis effect rendered by the parasitic impedances. The resulting modulated-signal is fed to the FoPI controller. The fixed controller parameters are meta-heuristically selected via a Particle-Swarm-Optimization (PSO) algorithm. The proposed control scheme exhibits rapid transits with improved damping in its response which aids in efficiently rejecting external disturbances such as load-transients and input-fluctuations. The superior robustness and time-optimality of the proposed control strategy is validated via experimental results.

• 대한수학회논문집
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• 제24권4호
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• pp.501-508
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• 2009

This paper presents a new representation algorithm which computes the representation for elements of a free group generated by two linear fractional transformations and also the justification of the algorithm in order to show how it operates correctly and efficiently according to inputs.

• 대한수학회보
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• 제56권1호
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• pp.1-12
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• 2019

For a finite poset $P=(X,{\preceq})$ the fractional weak discrepancy of P, denoted $wd_F(P)$, is the minimum value t for which there is a function $f:X{\rightarrow}{\mathbb{R}}$ satisfying (1) $f(x)+1{\leq}f(y)$ whenever $x{\prec}y$ and (2) ${\mid}f(x)-f(y){\mid}{\leq}t$ whenever $x{\parallel}y$. In this paper, we determine the range of the fractional weak discrepancy of (M, 2)-free posets for $M{\geq}5$, which is a problem asked in [9]. More precisely, we showed that (1) the range of the fractional weak discrepancy of (M, 2)-free interval orders is $W=\{{\frac{r}{r+1}}:r{\in}{\mathbb{N}}{\cup}\{0\}\}{\cup}\{t{\in}{\mathbb{Q}}:1{\leq}t<M-3\}$ and (2) the range of the fractional weak discrepancy of (M, 2)-free non-interval orders is $\{t{\in}{\mathbb{Q}}:1{\leq}t<M-3\}$. The result is a generalization of a well-known result for semiorders and the main result for split semiorders of [9] since the family of semiorders is the family of (4, 2)-free posets.

• Structural Engineering and Mechanics
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• 제73권6호
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• pp.725-735
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• 2020

The present investigation deals with the thermomechanical interactions in an orthotropic thermoelastic homogeneous body in the context of fractional order theory of thermoelasticity due to time harmonic sources. The application of a time harmonic concentrated and distributed sources has been considered to show the utility of the solution obtained. Assuming the disturbances to be harmonically time dependent, the expressions for displacement components, stress components and temperature change are derived in frequency domain. Numerical inversion technique has been used to determine the results in physical domain. The effect of frequency on various components has been depicted through graphs.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 2010년도 춘계학술대회
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• pp.129-138
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• 2010

For the fractional factorial designs, the resolution-IV designs can be used when we want to estimate the main effects and to investigate the structure of the non-negligible two-factor interaction effects, when the three-factor and higher order interaction effects are all negligible. However we need to add the additional treatment combination in order to identify the influential interactions for the resolution-IV fracrtional factorial designs. In this paper we investigate the statistical structure for 3-level resolution-IV designs constructed by fold-over scheme and introduce a method for analyzing the influential two-factor interactions.