• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.20 no.1
• /
• 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.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.3
• /
• pp.803-823
• /
• 2024

In this paper, we study the existence and uniqueness of solutions for the fractional time-varying delay integrodifferential equation with multi-point multi-term nonlocal and fractional integral boundary conditions by using fixed point theorems. The fractional derivative considered here is in the Caputo sense. Examples are provided to illustrate the results.

• The Journal of the Acoustical Society of Korea
• /
• v.22 no.8
• /
• pp.680-686
• /
• 2003

Digital waveguide model is a general method that is used in physical modeling of musical instruments. Wave motion is analyzed by time or by space in digital waveguide model. Because sampling is made via time, it is general that musical instrument model is described by wave motion of time. In this paper, we synthesized the musical instrument sound by adding instrument body model to the spatial based string model. In this way, we could improve sound quality and process musical instrument model's tone control variables effectively. We explained about delay error that happens in string and body in space based sampling and showed method to process fractional delay using FD (Fractional Delay)filter. Finally, we explained the relation between tone quality and number of delays. And we also compared the result with time base digital waveguide model.

• Journal of Applied and Pure Mathematics
• /
• v.4 no.3_4
• /
• pp.151-184
• /
• 2022

In the article, we handle with the existence and controllability results for fractional impulsive neutral functional integro-differential equation in Banach spaces. We have used advanced phase space definition for infinite delay. State dependent infinite delay is the main motivation using advanced version of phase space. The results are acquired using Schaefer's fixed point theorem. Examples are given to illustrate the theory.

• Proceedings of the IEEK Conference
• /
• 2003.07a
• /
• pp.366-369
• /
• 2003

현재 우리가 사용하고 있는 대부분의 시스템들은 대용량의 데이터를 송수신하고 있다. 대용량의 데이터를 전송하는 방법에는 여러방법이 있으나 한정되어 있는 대역폭을 사용하여 전송하기 위한 방법으로는 고속 전송을 사용한다. 많은 양의 데이터를 고속으로 전송을 하다 보면 여러가기 원인으로 인해 발생하는 지연에 대한 보정이 어려워 지게 된다. 이런 문제를 해결할 수 있는 방법중에 한가지가 바로 FDE(Fractional Delay Element)이다. FDE 는 1Clock 이하의 지연을 주는 소자로써 클럭 단위의 보정의 문제점을 해결한 것이다. 시스템 클럭을 고속으로 동작시키기에는 소자의 문제점이 있으나 FDE를 사용하면 시스템 클럭을 변화 없이 지연 보정을 할 수 있다. 본 논문에서는 VHDL 코딩과 FPGA 를 사용하여 FDE 를 구현 하였다. FDE 의 중요한 역할을 하는 FDF(Fractional Delay Filter)를 VHDL로 코딩을 하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.24 no.2
• /
• pp.229-242
• /
• 2020

Functional fractional differential inclusions with impulse effects in general Banach spaces are studied. We discuss the situation when the semigroup generated by the linear part is equicontinuous and the multifunction is Caratheodory. First, we define the PC-mild solutions for functional fractional semilinear impulsive differential inclusions. We then prove the existence of PC-mild solutions for such inclusions by using the fixed point theorem, multivalued properties and applications of NCHM (noncompactness Hausdorff measure). Eventually, we enhance the acquired results by giving an example.

• JSTS:Journal of Semiconductor Technology and Science
• /
• v.8 no.3
• /
• pp.179-192
• /
• 2008

A multiphase compensation method with mismatch linearization technique, is presented and demonstrated in a $\Sigma-\Delta$ fractional-N frequency synthesizer. An on-chip delay-locked loop (DLL) and a proposed delay line structure are constructed to provide multiphase compensation on $\Sigma-\Delta$ quantizetion noise. In the delay line structure, dynamic element matching (DEM) techniques are employed for mismatch linearization. The proposed $\Sigma-\Delta$ fractional-N frequency synthesizer is fabricated in a $0.18-{\mu}m$ CMOS technology with 2.14-GHz output frequency and 4-Hz resolution. The die size is 0.92 mm$\times$1.15 mm, and it consumes 27.2 mW. In-band phase noise of -82 dBc/Hz at 10 kHz offset and out-of-band phase noise of -103 dBc/Hz at 1 MHz offset are measured with a loop bandwidth of 200 kHz. The settling time is shorter than $25{\mu}s$.

• East Asian mathematical journal
• /
• v.36 no.1
• /
• pp.81-90
• /
• 2020

Many compartment models assume a kinetically homogeneous amount of materials that have well-stirred compartments. However, based on observations from such processes, they have been heuristically fitted by exponential or gamma distributions even though biological media are inhomogeneous in real environments. Fractional differential equations using a specific kernel in Pharmacokinetic/Pharmacodynamic (PKPD) model are recently introduced to account for abnormal drug disposition. We discuss a tumor growth inhibition (TGI) model using fractional-order derivative from it. This represents a tumor growth delay by cytotoxic agents and additionally show variations in the equilibrium points by the change of fractional order. The result indicates that the equilibrium depends on the tumor size as well as a change of the fractional order. We find that the smaller the fractional order, the smaller the equilibrium value. However, a difference of them is the number of concavities and this indicates that TGI over time profile for fitting or prediction should be determined properly either fractional order or tumor sizes according to the number of concavities shown in experimental data.

• Communications of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.171-177
• /
• 2018

In this research paper considering a differential equation with impulsive effect and dependent delay and applied Banach fixed point theorem using the impulsive condition to the impulsive fractional functional differential equation of an order ${\alpha}{\in}(1,2)$ to get an uniqueness solution. At last, theorem is verified by using a numerical example to illustrate the uniqueness solution.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.22 no.1
• /
• pp.63-74
• /
• 2018

In this paper, we study the initial value problem for neutral functional differential equations involving Caputo fractional derivative of order ${\alpha}{\in}(0,1)$ with infinite delay. Some sufficient conditions for the uniqueness and continuous dependence of solutions are established by virtue of fractional calculus and Banach fixed point theorem. Some results obtained showed that the solution was closely related to the conditions of delays and minor changes in the problem. An example is provided to illustrate the main results.