• 대한수학회지
• /
• 제36권5호
• /
• pp.855-890
• /
• 1999

Necessary and sufficient conditions on the weight functions u(.) and $\upsilon$(.) are derived in order that the fractional maximal operator $M\alpha,\;0\;\leq\;\alpha\;<\;1$, is bounded from the weighted amalgam space $\ell^s(L^p(\mathbb{R},\upsilon(x)dx)$ into $\ell^r(L^q(\mathbb{R},u(x)dx)$ whenever $1\leq s\leq r<\infty\;and\;1. The boundedness problem for the fractional intergral operator $I_{\alpha},0<\alpha\leq1$, is also studied.

• Communications for Statistical Applications and Methods
• /
• 제7권3호
• /
• pp.759-766
• /
• 2000

In order to design fractional factorial experiments which include some debarred combinations, we should select defining contrasts so that those combinations are to be excluded. Choi(1999) presented a method of selectign defining contrasts to construct orthogonal 3-level fractional factorial experiments which exclude some debarred combinations. In this paper, we extend Choi's method to general p-level fractional factorial experiments to select defining contrasts which cold exclude some debarred combinations.

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2005년도 춘계 학술발표회 논문집
• /
• pp.173-178
• /
• 2005

We derive an It${\hat{o}}$ formula for generalized functionals for the fractional Brownian sheet with arbitrary Hurst parameter ${H_1},\;H_2$ ${\epsilon}$ (0,1). As an application, we consider a stochastic integral representation for the local time of the fractional Brownian sheet.

• Journal of the Korean Statistical Society
• /
• 제34권4호
• /
• pp.281-295
• /
• 2005

We investigate the rate of convergence of the distribution of the maximum likelihood estimator (MLE) of an unknown parameter in the drift coefficient of a stochastic process described by a linear stochastic differential equation driven by a fractional Brownian motion (fBm). As a special case, we obtain the rate of convergence for the case of the fractional Ornstein- Uhlenbeck type process studied recently by Kleptsyna and Le Breton (2002).

• 대한수학회논문집
• /
• 제31권4호
• /
• pp.791-809
• /
• 2016

By introducing two fractional convolutions, we obtain the convolution theorems for fractional Fourier cosine and sine transforms. Applying these convolutions, we construct two Boehmian spaces and then we extend the fractional Fourier cosine and sine transforms from these Boehmian spaces into another Boehmian space with desired properties.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2001년도 ICCAS
• /
• pp.47.2-47
• /
• 2001

This paper is concerned with the limiting zeros, as the sampling period tends to zero, of a multivariable discrete-time system composed of an approximate fractional-order hold (AFROH), a continuous-time plant and a sampler in cascade. An approximate fractional-order hold is proposed to implement fractional-order hold (FROH) and is applied to instead of the zero-order hold (ZOH). The implementing problem of the fractional-order hold is overcome. The properties of the limiting zeros are studied and the location problem of them is solved. In addition, a stability condition of the zeros for sufficiently small sampling period is derived ...

• 대한수학회보
• /
• 제56권4호
• /
• pp.977-992
• /
• 2019

Mittag-Leffler stability of nonlinear fractional nabla difference systems is defined and the Lyapunov direct method is employed to provide sufficient conditions for Mittag-Leffler stability of, and in some cases the stability of, the zero solution of a system nonlinear fractional nabla difference equations. For this purpose, we obtain several properties of the exponential and one parameter Mittag-Leffler functions of fractional nabla calculus. Two examples are provided to illustrate the applicability of established results.

• Korean Journal of Mathematics
• /
• 제29권3호
• /
• pp.527-545
• /
• 2021

The aim of this article is to give a numerical method for solving Abel's general fuzzy linear integral equations with arbitrary kernel. The method is based on approximations of fractional integrals and Caputo derivatives. The convergence analysis for the proposed method is also given and the applicability of the proposed method is illustrated by solving some numerical examples. The results show the utility and the greater potential of the fractional calculus method to solve fuzzy integral equations.

• 호남수학학술지
• /
• 제42권4호
• /
• pp.653-665
• /
• 2020

In this paper, we establish new integral inequalities via Riemann-Liouville fractional integrals and Katugampola fractional integrals for the class of functions whose derivatives in absolute value are exponentially convex functions and exponentially s-convex functions in the second sense.

• Journal of applied mathematics & informatics
• /
• 제40권5_6호
• /
• pp.1167-1179
• /
• 2022

In this paper, we obtain some subsets of real numbers (ℝ) on which a fractional part function is defined as a real-valued continuous function. This gives rise to the analysis of the continuous properties of the fractional part function as a real-valued function. The analysis of fractional part function is helpful in the study of the dynamics of circle.