• 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.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.340-358
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• 2023

This article establishes an equality for the case of twice-differentiable convex functions with respect to the conformable fractional integrals. With the help of this identity, we prove sundry midpoint-type inequalities by twice-differentiable convex functions according to conformable fractional integrals. Several important inequalities are obtained by taking advantage of the convexity, the Hölder inequality, and the power mean inequality. Using the specific selection of our results, we obtain several new and well-known results in the literature.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.399-409
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• 2009

We study the weak convergence of various models to Fractional Brownian motion. First, we consider arima process and ON/OFF source model which allows for long packet trains and long inter-train distances. Finally, we figure out power spectrum density as a Fourier transform of autocorrelation function of arima model and binary signal model.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.203-210
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• 2015

We consider fractional Brownian motion and FARIMA process with Gaussian innovations and show that the suitably scaled distributions of the FARIMA processes converge to fractional Brownian motion in the sense of finite dimensional distributions. We figure out ACF function and estimate the self-similarity parameter H of FARIMA(0, d, 0) by using R/S method. Finally, we display power spectrum density of FARIMA process.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.619-628
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• 2023

In this paper, the fractional order time-varying linear dynamical systems are investigated by using a residual power series method. A residual power series method (RPSM) is constructed for this problem. The exact solution is obtained by the Laplace transform method and the analytical solution is calculated via the residual power series method (RPSM). As an application, some examples are tested to show the accuracy and efficacy of the proposed methods. The obtained result showed that the proposed methods are effective and accurate for this type of problem.

• Nuclear Engineering and Technology
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• v.52 no.9
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• pp.2017-2024
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• 2020

In this study, a fractional order proportional integral derivative (FOPID) controller is designed to create the reference power trajectory and to conquer the uncertainties and external disturbances. A fractional nonlinear model was utilized to describe the nuclear reactor dynamic behaviour considering thermal-hydraulic effects. The controller parameters were tuned using optimization method in Matlab/Simulink. The FOPID controller was simulated using Matlab/Simulink and the controller performance was evaluated for Hard variation of the reference power and compared with that of integer order a proportional integral derivative (IOPID) controller by two models of fractional neutron point kinetic (FNPK) and classical neutron point kinetic (CNPK). Also, the FOPID controller robustness was appraised against the external disturbance and uncertainties. Simulation results showed that the FOPID controller has the faster response of the control attempt signal and the smaller tracking error with respect to the IOPID in tracking the reference power trajectory. In addition, the results demonstrated the ability of FOPID controller in disturbance rejection and exhibited the good robustness of controller against uncertainty.

• ETRI Journal
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• v.33 no.1
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• pp.1-5
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• 2011

Downlink transmit power allocation schemes are proposed for soft fractional frequency reuse (FFR) in loose and tightly coordinated systems. The transmit powers are allocated so that the loss of spectral efficiency from the soft FFR is minimized, and the required cell edge user throughput is guaranteed. The effect of the soft FFR on spectral efficiency is evaluated depending on the power allocation schemes and the number of subbands. Results show that the loss of spectral efficiency from the soft FFR can be reduced by configuring an appropriate number of subbands in the loosely coordinated systems. In tightly coordinated systems, results show that the loss of spectral efficiency can be minimized regardless of the number of subbands due to its fast coordination.

• Earthquakes and Structures
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• v.13 no.5
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• pp.465-471
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• 2017

This work derives a generalized time fractional differential equation governing wave propagation in a radially vibrating non-classical cylindrical medium. The cylinder is made of a transversely isotropic hyperelastic John's material which obeys frequency-dependent power law attenuation. Employing the definition of the conformable fractional derivative, the solution of the obtained generalized time fractional wave equation is expressed in terms of product of Bessel functions in spatial and temporal variables; and the resulting wave is characterized by the presence of peakons, the appearance of which fade in density as the order of fractional derivative approaches 2. It is obtained that the transversely isotropic structure of the material of the cylinder increases the wave speed and introduces an additional term in the wave equation. Further, it is observed that the law relating the non-zero components of the Cauchy stress tensor in the cylinder under consideration generalizes the hypothesis of plane strain in classical elasticity theory. This study reinforces the view that fractional derivative is suitable for modeling anomalous wave propagation in media.

• Journal of Electrical Engineering and Technology
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• v.10 no.4
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• pp.1389-1399
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• 2015

This research suggests maximum power point tracking (MPPT) for the solar photovoltaic (PV) power scheme using a new constant voltage (CV) fractional order incremental conductance (FOINC) algorithm. The PV panel has low transformation efficiency and power output of PV panel depends on the change in weather conditions. Possible extracting power can be raised to a battery load utilizing a MPPT algorithm. Among all the MPPT strategies, the incremental conductance (INC) algorithm is mostly employed due to easy implementation, less fluctuations and faster tracking, which is not only has the merits of INC, fractional order can deliver a dynamic mathematical modelling to define non-linear physiognomies. CV-FOINC variation as dynamic variable is exploited to regulate the PV power toward the peak operating point. For a lesser scale photovoltaic conversion scheme, the suggested technique is validated by simulation with dissimilar operating conditions. Contributions are made in numerous aspects of the entire system, including new control algorithm design, system simulation, converter design, programming into simulation environment and experimental setup. The results confirm that the small tracking period and practicality in tracking of photovoltaic array.

• Journal of IKEEE
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• v.3 no.1 s.4
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• pp.39-49
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• 1999

This paper describes a 1 GHz, low-phase-noise CMOS fractional-N frequency synthesizer with an integrated LC VCO. The proposed frequency synthesizer, which uses a high-order delta-sigma modulator to suppress the fractional spurious tones at all multiples of the fractional frequency resolution offset, has 64 programmable frequency channels with frequency resolution of $f_ref/64$. The measured phase noise is as low as -110 dBc/Hz at a 200 KHz offset frequency from a carrier frequency of 980 MHz. The reference sideband spurs are -73.5 dBc. The prototype is implemented in a $0.5{\mu}m$ CMOS process with triple metal layers. The active chip area is about $4mm^2$ and the prototype consumes 43 mW, including the VCO buffer power consumption, from a 3.3 V supply voltage.