• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.429-437
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• 2014

Motivated by the recent investigations of several authors, in this paper we present a generalization of a result obtained recently by Choi et al. ([3]) involving hypergeometric identities. The result is obtained by suitably applying fractional calculus method to a generalization of the hypergeometric transformation formula due to Kummer.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.851-857
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• 2011

By using Malliavin calculus, we study a central limit theorem of the cross variation related to fractional Brownian sheet with Hurst parameter H = ($H_1$, $H_2$) such that 1/4 < $H_1$ < 1/2 and 1/4 < $H_2$ < 1/2.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.827-844
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• 2016

Here, in this paper, we aim at establishing some new unified integral and differential formulas associated with the $\bar{H}$-function. Each of these formula involves a product of the $\bar{H}$-function and Srivastava polynomials with essentially arbitrary coefficients and the results are obtained in terms of two variables $\bar{H}$-function. By assigning suitably special values to these coefficients, the main results can be reduced to the corresponding integral formulas involving the classical orthogonal polynomials including, for example, Hermite, Jacobi, Legendre and Laguerre polynomials. Furthermore, the $\bar{H}$-function occurring in each of main results can be reduced, under various special cases.

• Journal of the Semiconductor & Display Technology
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• v.23 no.2
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• pp.60-64
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• 2024

The threshold voltage shift in thin-film transistors (TFTs) is modeled using stretched-exponential (SE) and stretched-hyperbola (SH) functions. These models are derived by introducing empirical parameters into reaction rate equations that describe defect generation or charge trapping caused by hydrogen diffusion in the dielectric or interface. Separately, the dielectric relaxation phenomena are also described by the same reaction rate equations based on defect diffusion. Dielectric relaxation was initially modeled using the SE model, and various models have been proposed using fractional calculus. In this study, the characteristics of the threshold voltage shift and the dielectric relaxation phenomena are compared and analyzed to explore the applicability of analytical models used in the field of dielectric relaxation, in addition to the conventional SE and SH models.

• International Journal of Control, Automation, and Systems
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• v.4 no.6
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• pp.775-781
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• 2006

An intelligent optimization method for designing Fractional Order PID(FOPID) controllers based on Particle Swarm Optimization(PSO) is presented in this paper. Fractional calculus can provide novel and higher performance extension for FOPID controllers. However, the difficulties of designing FOPID controllers increase, because FOPID controllers append derivative order and integral order in comparison with traditional PID controllers. To design the parameters of FOPID controllers, the enhanced PSO algorithms is adopted, which guarantee the particle position inside the defined search spaces with momentum factor. The optimization performance target is the weighted combination of ITAE and control input. The numerical realization of FOPID controllers uses the methods of Tustin operator and continued fraction expansion. Experimental results show the proposed design method can design effectively the parameters of FOPID controllers.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.7
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• pp.1014-1019
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• 2013

Signal processing techniques based on fractional order calculus have been successfully applied in analyzing heavy-tailed non-Gaussian signals. It was found that the surface EMG signals from the muscles having nuero-muscular disease are best modeled by using the heavy-tailed non-gaussian random processes. In this regard, this paper describes an application of digital fractional order lowpass differentiators(FOLPD, weighted FOLPD) based on the fractional order calculus in detecting peaks of surface EMG signal. The performances of the FOLPD and WFOLPD are analyzed based on different filter length and varying MUAP wave shape from recorded and simulated surface EMG signals. As a results, the WFOLPD showed better SNR improving factors than the existing WLPD and to be more robust under the various surface EMG signals.

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.127-145
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• 2009

In this paper we introduce a new subclass $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ of analytic and multivalent functions with negative coefficients using fractional calculus operators. Connections to the well known and some new subclasses are discussed. A necessary and sufficient condition for a function to be in $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ is obtained. Several distortion inequalities involving fractional integral and fractional derivative operators are also presented. We also give results for radius of starlikeness, convexity and close-to-convexity and inclusion property for functions in the subclass. Modified Hadamard product, application of class preserving integral operator and other interesting properties are also discussed.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.557-573
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• 2021

In this present paper, we consider four integrals and differentials containing the Gauss' hypergeometric ₂F₁(x) function in the kernels, which extend the classical Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators. Formulas (images) for compositions of such generalized fractional integrals and differential constructions with the n-times product of the generalized modified Bessel function of the second type are established. The results are obtained in terms of the generalized Lauricella function or Srivastava-Daoust hypergeometric function. Equivalent assertions for the Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential are also deduced.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1115-1125
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• 2023

This paper deals with the controllability of linear and nonlinear generalized fractional dynamical systems in finite dimensional spaces. The results are obtained by using fractional calculus, Mittag-Leffler function and Schauder's fixed point theorem. Observability of linear system is also discussed. Examples are given to illustrate the theory.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.125-138
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• 2018

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.