• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.197-223
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• 2021

In this paper, we investigate existence, uniqueness and four different types of Ulam's stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and $Krasnosel^{\prime}ski{\breve{i}}{^{\prime}}s$ fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.513-532
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• 2022

This paper deals with the stability of solutions to 𝜓-Hilfer fractional differential systems. We derive the fundamental solution for the system by using the generalized Laplace transform and the Mittag-Leffler function with two parameters. In addition, we obtained some necessary conditions on the stability of the solutions to linear fractional differential systems for homogeneous, non-homogeneous and non-autonomous cases. Numerical examples are also given to illustrate the behavior of solutions.

• 한국축산식품학회지
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• 제43권2호
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• pp.220-231
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• 2023

Although omega-3 fatty acids including docosahexaenoic acid (DHA) contain various health-promoting effects, their poor aqueous solubility and stability make them difficult to be induced in dairy foods. The aims of this research were to manufacture casein derivative-based delivery system using acid-induced gelation method with glucono-σ-lactone and to investigate the effects of production variables, such as pH and charged amount of linoleic acid, on the physicochemical properties of delivery systems and oxidative stability of DHA during storage in model milk. Covalent modification with linoleic acid resulted in the production of casein derivatives with varying degrees of modification. As pH was reduced from 5.0 to 4.8 and the charged amount of linoleic acid was increased from 0% to 30%, an increase in particle size of casein derivative-based delivery systems was observed. The encapsulation efficiency of DHA was increased with decreased pH and increased charged amount of linoleic acid. The use of delivery system for DHA resulted in a decrease in the development of primary and secondary oxidation products. An increase in the degree of modification of casein derivatives with linoleic acid resulted in a decrease in the formation of primary and secondary oxidation products than of free DHA indicating that delivery systems could enhance the oxidative stability of DHA during storage in model milk. In conclusions, casein derivatives can be an effective delivery system for DHA and charged amount of linoleic acid played a key role determining the physicochemical characteristics of delivery system and oxidative stability of DHA.

• 대한수학회보
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• 제47권6호
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• pp.1225-1234
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• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.1017-1034
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• 2023

In this paper, we work two different problems. First, we investigate a new class of fractional differential equations involving Caputo sequential derivative with some (e₁, e₂, θ)-periodic conditions. The existence and uniqueness of solutions are proven. The stability of solutions is also discussed. The second part includes studying traveling wave solutions of a conformable fractional Korteweg-de Vries-Burger (KdV Burger) equation through the Tanh method. Graphs of some of the waves are plotted and discussed, and a conclusion follows.

• 대한조선학회논문집
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• 제46권4호
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• pp.391-397
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• 2009

In this paper, longitudinal static stability is investigated, which is an essential requirement for the safety and the performance of the human powered hydrofoil boat (HPHB). In case a disturbance changes the trim angle of the boat, the derivative of the moment about the center of gravity must be negative in order to make the boat to be stable. The equation to evaluate the longitudinal static stability of the EPISODE, a HPHB of Chungnam National University with a height controlling system(HCS) is derived. From the derivative it is confirmed that a longitudinal and vertical position of the center of gravity is important for a HPHB. The range of a trim angle while the boat is foil-born was found with a HCS under the condition of mechanical restraint. And it is confirmed that the longitudinal static stability is satisfied for EPISODE in certain range of a trim angle. It is also shown that the longitudinal static stability and a range of the trim angle can be determined from the principal dimensions of a HPHB, therefore, it can be applied from the stage of the conceptual design of HPHB.

• 대한기계학회논문집B
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• 제27권8호
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• pp.1122-1133
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• 2003

Numerical characteristics of implicit upwind schemes, such as upwind ADI, line Gauss-Seidel (LGS) and point Gauss-Seidel (LU) algorithms, for Navier-Stokes equations have been investigated. Time-derivative preconditioning method was applied for efficient convergence at low Mach/Reynolds number regime as well as at large grid aspect ratios. All the algorithms were expressed in approximate factorization form and von Neumann stability analysis was performed to identify stability characteristics of the above algorithms in the presence of high grid aspect ratios. Stability analysis showed that for high aspect ratio computations, the ADI and LGS algorithms showed efficient damping effect up to moderate aspect ratio if we adopt viscous preconditioning based on min-CFL/max-VNN time-step definition. The LU algorithm, on the other hand, showed serious deterioration in stability characteristics as the grid aspect ratio increases. Computations for several practical applications also verified these results.

• 한국항공우주학회지
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• 제40권11호
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• pp.948-956
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• 2012

본 논문에서는 SDM 형상의 세로와 방향의 안정성 미계수를 예측하였다. 피치와 요 방향에 대한 강제조화 진동운동을 이용하여 정적 및 동적 미계수를 한 번에 계산하였다. 계산은 비정상 해석을 위한 이중시간 적분법을 적용한 3차원 Euler 해석자를 사용하여 수행하였다. 본 연구에서는 마하수뿐만 아니라 다양한 운동 변수에 따른 미계수를 예측하였다. 예측된 결과는 이전에 발표된 수치적, 실험적 연구 결과들과 비교하여 검증하였다.

• 대한수학회보
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• 제54권4호
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• pp.1309-1321
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• 2017

In this paper, we present a practical Mittag Leffler stability for fractional-order nonlinear systems depending on a parameter. A sufficient condition on practical Mittag Leffler stability is given by using a Lyapunov function. In addition, we study the problem of stability and stabilization for some classes of fractional-order systems.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.793-809
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• 2021

This paper gives sufficient conditions to ensure the existence and stability of solutions for generalized nonlinear fractional integrodifferential equations of order α (1 < α < 2). The main theorem asserts the stability results in a weighted Banach space, employing the Krasnoselskii's fixed point technique and the existence of at least one mild solution satisfying the asymptotic stability condition. Two examples are provided to illustrate the theory.