• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제20권1호
• /
• pp.51-82
• /
• 2016

In view of ideas for semigroups, fractional calculus, resolvent operator and Banach contraction principle, this manuscript is generally included with existence and controllability (EaC) results for fractional neutral integro-differential systems (FNIDS) with state-dependent delay (SDD) in Banach spaces. Finally, an examples are also provided to illustrate the theoretical results.

• Communications for Statistical Applications and Methods
• /
• 제13권3호
• /
• pp.587-605
• /
• 2006

Recent results in applied statistics have shown that the presence of periodicities in time series may influence the estimation and testing of the fractional differencing parameter. In this article, we provide further evidence on the issue by using several procedures of fractional integration. The results show that in the presence of periodicities, the order of integration can be erroneously detected. An empirical application in the context of seasonal data is also carried out at the end of the article.

• Kyungpook Mathematical Journal
• /
• 제61권2호
• /
• pp.383-393
• /
• 2021

In this paper, numerical techniques are presented for solving initial value problems of fractional differential equations with variable coefficients. The method is derived by applying a Taylor vector approximation. Moreover, the operational matrix of fractional integration of a Taylor vector is provided in order to transform the continuous equations into a system of algebraic equations. Furthermore, numerical examples demonstrate that this method is applicable and accurate.

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

• 대한전자공학회논문지TC
• /
• 제42권7호
• /
• pp.35-40
• /
• 2005

본 논문에서는 900MHz 대역 중저속 무선 통신용 칩에 이용되는 3차 ${\Delta}{\sum}$ modulator를 사용한 Fractional-N PLL 주파수 합성기를 설계 및 제작하였다 우수한 위상노이즈 특성을 얻기 위해 노이즈 특성이 좋은LC VCO를 사용하였다. 그리고 고착시간을 줄이기 위해서 Charge Pump의 펌핑 전류를 주파수 천이 값에 따라 조절할 수 있도록 제작하였고 PFD의 참조 주파수를 3MHz까지 높였다. 또한 참조 주파수를 높이는 동시에 PLL의 최소 주파수 천이 간격을 10KHz까지 줄일 수 있도록 하기위하여 36/37 Fractional-N 분주기를 제작하였다. Fractional Spur를 줄이기 위해서 3차 ${\Delta}{\sum}$ modulator를 사용하였다. 그리고 VCO, Divider by 8 Prescaler, PFD, 및 Charge Pump는 0.25um CMOS공정으로 제작되었으며, 루프 필터는 외부 컴포넌트를 이용한 3차RC 필터로 제작되었다. 그리고 Fractional-N 분주기와 3차 ${\Delta}{\sum}$ modulator는 VHDL 코드로 작성되었으며 Xilinx Spartan2E을 사용한 FPGA 보드로 구현되었다. 측정결과 PLL의 출력 전력은 약 -11dBm이고, 위상노이즈는 100kHz offset 주파수에서 -77.75dBc/Hz이다. 최소 주파수 간격은 10kHz이고, 최대 주파수 천이는 10MHz이고, 최대 주파수 변이 조건에서 고착시간은 약 800us이다.

• Structural Engineering and Mechanics
• /
• 제63권1호
• /
• pp.89-102
• /
• 2017

In this work, we present a theoretical framework to study the thermovisco-elastic responses of homogeneous, isotropic and perfectly conducting medium subjected to inclined load. Based on recently developed generalized thermoelasticity theory with fractional order strain, the two-dimensional governing equations are obtained in the context of generalized magnetothermo-viscoelasticity theory without energy dissipation. The Kelvin-Voigt model of linear viscoelasticity is employed to describe the viscoelastic nature of the material. The resulting formulation of the field equations is solved analytically in the Laplace and Fourier transform domain. On the application of inclined load at the surface of half-space, the analytical expressions for the normal displacement, strain, temperature, normal stress and tangential stress are derived in the joint-transformed domain. To restore the fields in physical domain, an appropriate numerical algorithm is used for the inversion of the Laplace and Fourier transforms. Finally, we have demonstrated the effect of magnetic field, viscosity, mechanical relaxation time, fractional order parameter and time on the physical fields in graphical form for copper material. Some special cases have also been deduced from the present investigation.

• Structural Engineering and Mechanics
• /
• 제87권4호
• /
• pp.305-315
• /
• 2023

The idea of the combination of the fractional-order operators with the brain emotional learning-based intelligent controller (BELBIC) is developed for implementation in seismic-excited structures equipped with active mass damper (AMD). For this purpose, a new design framework of the mentioned combination namely fractional-order BEBIC (FOBELBIC) is proposed based on a modified-teaching-learning-based optimization (MTLBO) algorithm. The seismic performance of the proposed controller is then evaluated for a 15-story building equipped with AMD subjected to two far-field and two near-field earthquakes. An optimal BELBIC based on the MTLBO algorithm is also introduced for comparison purposes. In comparison with the structure equipped with a passive tuned mass damper (TMD), an average reduction of 44.7% and 42.8% are obtained in terms of the maximum absolute and RMS top floor displacement for FOBELBIC, while these reductions are obtained as 30.4% and 30.1% for the optimal BELBIC, respectively. Similarly, the optimal FOBELBIC results in an average reduction of 42.6% and 39.4% in terms of the maximum absolute and RMS top floor acceleration, while these reductions are given as 37.9% and 30.5%, for the optimal BELBIC, respectively. Consequently, the superiority of the FOBELBIC over the BELBIC is concluded in the reduction of maximum and RMS seismic responses.

• Journal of applied mathematics & informatics
• /
• 제31권1_2호
• /
• pp.221-228
• /
• 2013

The method of upper and lower solutions and the generalized quasilinearization technique is developed for the existence and approximation of solutions to boundary value problems for higher order fractional differential equations of the type $^c\mathcal{D}^qu(t)+f(t,u(t))=0$, $t{\in}(0,1),q{\in}(n-1,n],n{\geq}2$ $u^{\prime}(0)=0,u^{\prime\prime}(0)=0,{\ldots},u^{n-1}(0)=0,u(1)={\xi}u({\eta})$, where ${\xi},{\eta}{\in}(0,1)$, the nonlinear function f is assumed to be continuous and $^c\mathcal{D}^q$ is the fractional derivative in the sense of Caputo. Existence of solution is established via the upper and lower solutions method and approximation of solutions uses the generalized quasilinearization technique.

• 한국전산유체공학회지
• /
• 제8권3호
• /
• pp.50-55
• /
• 2003

Recent numerical simulation has a tendency to require the higher-order accuracy in time, as well as in space. This tendency is more true in LES and acoustic noise simulation. In the present work, the accuracy of a Fractional step method, which is widely used in LES simulation, has been increased to the fourth-order accurate compact Pade discretization. To validate the present code, the flow-field past a cylinder was simulated and compared with experiment. A good agreement with experiment was achieved.

• 품질경영학회지
• /
• 제38권1호
• /
• pp.42-51
• /
• 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 combinations in order to identify the influential interactions for the resolution-IV fractional 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.