• Wind and Structures
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• 제28권6호
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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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• 제61권1호
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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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• 제25권3호
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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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• 제13권5호
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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.

• 한국자원식물학회:학술대회논문집
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• 한국자원식물학회 2010년도 정기총회 및 추계학술발표회
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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.

• 한국토양비료학회지
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• 제6권4호
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• pp.221-226
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• 1973

현(現) 비료(肥料) 공정규격(公定規格)에 보증성분(保證成分)이 미달(未達)되는 규회석(珪灰石)의 비효(肥效) 및 규회석(珪灰石)의 가용(可溶) 규산분석법(珪酸分析法)을 검토(檢討)코져, 가용규산함량(可溶珪酸含量)이 상이(相異)한 수종(數種)의 규회석(珪灰石) 및 규회석(珪灰石)과 가용성규산(可溶性珪酸)을 함유(含有)하지 않은 암석(岩石)의 혼합분말(混合粉末)을 광재(鑛滓)와 대조(對照)하여 벼에 대한 재배시험(栽培試驗)을 수행(遂行)하여 규산(珪酸)의 흡수량(吸收量)을 조사(調査)하고, 공시(供試) 규회석(珪灰石)을 수종(數種)의 완형용액(緩衡溶液)에 침출(浸出)하여 규산가용율(珪酸可溶率)과 식물체(植物體)가 흡수(吸收)한 규산함량(珪酸含量)과 상관관계(相關關係) 및 규회석(珪灰石)의 X-선회절분석(線回折分析)을 하여 다음과 같은 결과(結果)를 얻었다. 1. 가용성(可溶性) 규산함량(珪酸含量)(N/2 HCl)이 높은 규회석(珪灰石)일수록 식물체중의 규산함량 및 흡수량(吸收量)을 증가(增加)시켰다. 2. 광재(鑛滓) 처리구(處理區)의 벼 짚중(中) 규산흡수량(珪酸吸收量)은 가용성(可溶性) 규산함량(珪酸含量)이 4.1%인 규회석분말구(珪灰石粉末區)와 같이 가장 낮았다. 3. 가용성(可溶性) 규산함량(珪酸含量)이 높은 규회석(珪灰石)에 잡석(雜石)을 혼합(混合)하여 시비(施肥)하여도 수도체(水稻體)의 규산함량(珪酸含量)은 동량(同量)의 가용성규산함량(可溶性珪酸含量)을 함유(含有)한 규회석(珪灰石)과 같은 효과이었다. 4. 각종(各種) 완형용액(緩衡溶液)에 침출(浸出)된 가용규산(可溶珪酸)과 짚중(中) 규산함량(珪酸含量) 및 흡수량(吸收量)과는 고도(高度)의 유의성(有意性)이 있는 정(正)의 상관(相關)이었으며 N/2염산(鹽酸) 침출규산(浸出珪酸) 분석법(分析法)도 규회석(珪灰石)의 규산분석법(珪酸分析法)으로써 충분(充分)히 사용(使用)될 수 있는 방법(方法)이었다. 5. 규회석(珪灰石)의 X-선(線) 회절(回折)은 규회석(珪灰石)의 조성(造成)을 찾아낼 수 있으며, 결정(結晶)이 불량(不良)한 규회석(珪灰石) 일수록 가용규산함량(可溶珪酸含量)이 높았다.