• The Journal of the Korea institute of electronic communication sciences
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• v.16 no.3
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• pp.503-510
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• 2021

This study intends to apply the mathematical method of fractional order differentiation to a controller that controls the response of the system. Therefore, we design integrator for the fractional index by converting it into discrete time to construct a controller. The IP controller composes an integral controller for errors and the proportional controller applies only the system output. The controller is designed by using the fractional order integrator to the integral controller of the IP controller. First, the performance of the PI controller and the IP controller is compared, and the designed controller is applied to the speed control of the motor. As a result, the motor output speed was uniformed and precise control performance could be obtained. It was confirmed that the speed error in the steady state is within 0.1 [%], and it has precise and uniform speed control performance without overshoot.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.52 no.9
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• pp.454-459
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• 2003

Conventional integral-slot design in permanent magnet(PM) motor tends to have a high cogging torque and large end turns, which contribute to copper losses. The fractional-slot design is effective compared to integral-slot design in the cogging torque and electromotive force(EMF) waveform. The effectiveness of fractional slot can be maximized by selecting optimal pole to slot ratio. This paper presents the effect of pole to slot ratio on the cogging torque and EMF waveform in the PM motor with fractional-slot. The effectiveness of the proposed designs has been confirmed by comparing waveform of EMF. cogging torque and torque ripple between conventional and new models.

• 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.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.153-159
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• 2005

In the present paper, we obtain two Theorems connecting the unified fractional integral operators and the Laplace transform. Due to the presence of a general class of polynomials, the multivariable H-function and general functions ${\theta}$ and ${\phi}$ in the kernels of our operators, a large number of (new and known) interesting results involving simpler polynomials (which are special cases of a general class of polynomials) and special functions involving one or more variables (which are particular cases of the multivariable H-function) obtained by several authors and hitherto lying scattered in the literature follow as special cases of our findings. Thus the Theorems obtained by Srivastava et al. [9] follow as simple special cases of our findings.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.423-436
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• 2018

We aim to establish certain Saigo hypergeometric fractional integral formulas for a finite product of the generalized k-Bessel functions, which are also used to present image formulas of several integral transforms including beta transform, Laplace transform, and Whittaker transform. The results presented here are potentially useful, and, being very general, can yield a large number of special cases, only two of which are explicitly demonstrated.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.341-349
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• 2019

This paper is concerned to investigate M-Wright function, which was earlier known as transcendental function of the Wright type. M-Wright function is a special case of the Wright function given by British mathematician (E.Maitland Wright) in 1933. We have explored the cosequences of Riemann-Liouville Integral and Differential operators on M-Wright function. We have also evaluated integral transforms of the M-Wright function.

• 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.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.127-147
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• 2019

In this paper we establish some new explicit solutions for impulsive linear fractional differential equations with impulses at fixed times, which provides a handy tool in deriving singular integral-sum inequalities and an impulsive fractional comparison principle. Thus we study the Mittag-Leffler stability of impulsive differential equations with the Caputo fractional derivative by using the impulsive fractional comparison principle and piecewise continuous functions of Lyapunov's method. Also, we give some examples to illustrate our results.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.305-316
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• 2022

We study the existence and uniqueness of solutions for a class of boundary value problems of nonlinear fractional order differential equations involving the Caputo fractional derivative by employing the Banach's contraction principle and the Schauder's fixed point theorem. In addition, an example is given to demonstrate the application of our main results.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.257-273
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• 2010

One can construct a theory of probability of fractional order in which the exponential function is replaced by the Mittag-Leffler function. In this framework, it seems of interest to generalize some useful classical mathematical tools, so that they are more suitable in fractional calculus. After a short background on fractional calculus based on modified Riemann Liouville derivative, one summarizes some definitions on probability density of fractional order (for the motive), and then one introduces successively fractional Euler's integrals (first and second kind) and fractional Hermite polynomials. Some properties of the Gaussian density of fractional order are exhibited. The fractional probability so introduced exhibits some relations with quantum probability.