• Wind and Structures
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• v.28 no.6
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• pp.347-354
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• 2019

This study provides an approximate analytical solution to the fractional vibration problem of thin plate governing anomalous motion of plate subjected to in-plane loads. The method of variable separable is employed to transform the fractional partial differential equations under consideration into a fractional ordinary differential equation in temporal variable and a bi-harmonic plate equation in spatial variable. The technique of conformable fractional derivative is utilized to solve the resulting fractional differential equation and the approach of finite sine integral transform method is used to solve the accompanying bi-harmonic plate equation. The deflection field which measures the transverse displacement of the plate is expressed in terms of product of Bessel and trigonometric functions via the temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem of thin plate in literature. This work shows that conformable fractional derivative is an efficient mathematical tool for tracking analytical solution of fractional partial differential equation governing anomalous vibration of thin plates.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.139-153
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• 2021

In this paper, we study the existence of positive solutions for a class of conformable fractional differential equations with integral boundary conditions. By using the properties of Green's function with the fixed point theorem in a cone, we prove the existence of a positive solution. We also provide some examples to illustrate our results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.3
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• pp.132-148
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• 2021

The modified F-expansion method is used to construct analytical solutions of the foam drainage equation with time- and space-fractional derivatives. The conformable derivatives are considered as spacial and temporal ones. As a result, some analytical exact solutions including kink, bright-dark soliton, periodic and rational solutions are obtained.

• Earthquakes and Structures
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• v.13 no.5
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• pp.465-471
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• 2017

This work derives a generalized time fractional differential equation governing wave propagation in a radially vibrating non-classical cylindrical medium. The cylinder is made of a transversely isotropic hyperelastic John's material which obeys frequency-dependent power law attenuation. Employing the definition of the conformable fractional derivative, the solution of the obtained generalized time fractional wave equation is expressed in terms of product of Bessel functions in spatial and temporal variables; and the resulting wave is characterized by the presence of peakons, the appearance of which fade in density as the order of fractional derivative approaches 2. It is obtained that the transversely isotropic structure of the material of the cylinder increases the wave speed and introduces an additional term in the wave equation. Further, it is observed that the law relating the non-zero components of the Cauchy stress tensor in the cylinder under consideration generalizes the hypothesis of plane strain in classical elasticity theory. This study reinforces the view that fractional derivative is suitable for modeling anomalous wave propagation in media.

• Proceedings of the Plant Resources Society of Korea Conference
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• 2010.10a
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• pp.15-15
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• 2010

Ginseng contained many different kinds of saponin which was the most valuable for people, but its yield cannot satisfy the demand using traditional extract methods. Enzyme transformation is a conformable and highly performed method which was fit for today. A ${\beta}$-glucosidase producing bacterium ($DCY51^T$) was isolated from Korean fermented-vegetable food kimchi. The 16S rRNA gene sequence analysis revealed that the strain $DCY51^T$ belongs to the genus Lactobacillus. The highest sequence similarity was found with Lactobacillus paracollinoides LMG $22473^T$ and Lactobacillus collinoides LMG $9194^T$ with levels of 16S rDNA similarity of 97.4% and 97.3%, respectively. Based on the above results the strain $DCY51^T$ placed in the genus Lactobacillus and proposed a new species, Lactobacillus kimchicus sp. nov. $DCY51^T$ (= KCTC $12976^T$ = JCM $15530^T$). It was culture solution reacted with Red Ginseng extract and $Rb_1$, respectively. The medium of bacteria was the liquid of MRS, the temperatures of growing and reacting between bacteria liquid and saponin were samely $37^{\circ}C$, there spective reacting time were 12 hours and 48 hours. Thus we got different saponins, and TLC and HPLC analysis showed that: enzyme respectively reacted with $Rb_1$ and Red Ginseng extract got the transformed saponin, respectively. The polarity position in TLC was a little higher than Rd; and the polarity position was the same as that of Compound K's, the saponin obtained from HPLC and other experimental results was not Compound K. The constitution of its saponin was hoped to be further confirmed.

• Korean Journal of Soil Science and Fertilizer
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• v.6 no.4
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• pp.221-226
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• 1973

In order to investigate the silica effect of insufficient wollastonite to the official standard (above than 15% of suluble silica (N/2 HCl) on rice plant as silica fertilizer, 9 kinds of wollastonites and slag were adopted to examine the amount of silica absorbed by rice straw during growing period, and soluble silica of wollastonites extracted by 7 buffer solutions were compared with silica content in rice straw. Crystalls of ingredient in wollastonite ores were identified by X-ray diffractometer. The results were that silica content of rice plant at growing stages were increased as same ratio of soluble silica. content in wollastonite. Wollastonite containing more than 10% of souble silica (N/2 HCl) could be applied as fertilizer because absorbed amount of silica by rice plant from them are higher than from slag which contained 30% of soluble silica. Wollastonite powder mixed with impure ores in which soluble silica could not be extracted had the same effect on silica absorption of straw as wollastonite powder which contained conformable amount of soluble silica. The soluble silica of wollastonite extracted by buffer solutions (2% citric acid, N. NaOAc, N. $NH_4OAc$, Petermann solution, 0.1M. EDTA, and Hot water) had high significant relation to silica content in rice straw, but soluble silica extracted N/2 hydrochloric acid solutilon, also, had deep relation to them in rice straw. The adequate solution to extract silica from wollastonites is N/2 hydrochloric acid solution because its extracted silia amount is much higher than other solution (about one hundred times) and can be determined by gravimetric analysis. X-ray diffraction pattern would identify qualitatively purity of wollastonite, and large amount of soluble silica was extracted from wollastonite which was appeared to be weathered.