• Journal of Power Electronics
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• v.13 no.6
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• pp.1008-1015
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• 2013

By using fractional calculus and the circuit-averaging technique, the modeling and analysis of a Buck converter with fractional order inductor and fractional order capacitor in discontinuous conduction mode (DCM) operations is investigated in this study. The equivalent averaged circuit model of the fractional order Buck converter in DCM operations is established. DC analysis is conducted by using the derived DC equivalent circuit model. The transfer functions from the input voltage to the output voltage, the duty cycle to the output voltage, the input impedance, and the output impedance of the fractional order Buck converter in DCM operations are derived from the corresponding AC-equivalent circuit model. Results show that the DC equilibrium point, voltage ratio, and all derived transfer functions of the fractional order Buck converter in DCM operations are affected by the inductor order and/or capacitor order. The fractional order inductor and fractional order capacitor are designed, and PSIM simulations are performed to confirm the correctness of the derivations and theoretical analysis.

• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.73-116
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• 2020

The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences. Various operators of fractional-order derivatives as well as fractional-order integrals do indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this survey-cum-expository article is to present a brief elementary and introductory overview of the theory of the integral and derivative operators of fractional calculus and their applications especially in developing solutions of certain interesting families of ordinary and partial fractional "differintegral" equations. This general talk will be presented as simply as possible keeping the likelihood of non-specialist audience in mind.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.159-164
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• 2017

This paper deals with linear impulsive differential equations involving the Caputo fractional derivative. We provide exact solutions of nonhomogeneous linear impulsive fractional differential equations with constant coefficients by means of the Mittag-Leffler functions.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.57-64
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• 2021

In this paper we deal with the embedding inclusions on the fractional Orlicz-Sobolev spaces which are crucial roles for studying the theories of the partial differential equations. We get some properties and theories of the embedding inclusions on the fractional Orlicz-Sobolev spaces.

• Journal of Applied and Pure Mathematics
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• v.5 no.5_6
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• pp.315-346
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• 2023

We present a variety of univariate and multivariate left and right side Hardy type fractional inequalities, many of them under convexity, and other also of L_p type, p ≥ 1, in the setting of generalized Hilfer and Prabhakar fractional Calculi.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.3
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• pp.540-545
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• 2013

The Fractional Fourier transform, as a generalization of the classical Fourier Transform, was first introduced in quantum mechanics. Because of its simple and useful properties of Fractional Fourier transform in time-frequency plane, various research results in sonar and radar signal processing have been introduced and shown superior results to conventional method utilizing Fourier transform until now. In this paper, we applied Fractional Fourier transform to sonar signal processing to detect and separate the overlapping linear frequency modulated signals. Experimental results show that received overlapping LFM(Linear Frequency Modulation) signals can be detected and separated effectively in Fractional Fourier transform domain.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.11 no.8
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• pp.1558-1563
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• 2007

In this paper, phase-locked loop (PLL) of a combinational architecture consisting of an adaptive bandwidth and fractional-N is presented to improve performances and reduce the order of ${\Delta}{\Sigma}$ modulator while maintaining equivalent or better performance with fast locking. The architecture of adaptive bandwidth PLL was simulated by HSPICE using 0.35m CMOS parameters. The behavioral simulation of the proposed adaptive bandwidth fractional-N PLL with a ${\Delta}{\Sigma}$ modulator was carried out by using MatLab to determine if the architecture could achieve the objectives. The HSPICE simulation showed that this type of PLL was able to fast locking, and reduce fractional spurs about 20dB.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.283-291
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• 2007

A simple graph G is said to be fractional n-factor-critical if after deleting any n vertices the remaining subgraph still has a fractional perfect matching. For fractional n-factor-criticality, in this paper, one necessary and sufficient condition, and three sufficient conditions related to maximum matching, complete closure are given.

• East Asian mathematical journal
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• v.17 no.1
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• pp.135-146
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• 2001

Several families of infinite series were summed recently by means of certain operators of fractional calculus(that is, calculus of derivatives and integrals of any real or complex order). In the present sequel to this recent work, it is shown that much more general classes of infinite sums can be evaluated without using fractional calculus. Some other related results are also considered.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.265-275
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• 2006

In this paper, we introduce a fractional domination game arising from fractional domination problems on graphs and focus on its balancedness and concavity. We first characterize the core of the fractional domination game and show that its core is always non-empty taking use of dual theory of linear programming. Furthermore we study concavity of this game.