• Korean Journal of Mathematics
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• v.27 no.2
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• pp.357-374
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• 2019

In this paper, first we obtain some inequalities of Hadamard type for (h - m)-convex functions via Caputo k-fractional derivatives. Secondly, two integral identities including the (n + 1) and (n+ 2) order derivatives of a given function via Caputo k-fractional derivatives have been established. Using these identities estimations of Hadamard type integral inequalities for the Caputo k-fractional derivatives have been proved.

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.103-112
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• 2022

A definition of fractional vector cross product of two vectors in Euclidean 3-space is presented. The formulas for Euclidean norm of the fractional vector cross product of two vectors, and for fractional triple vector cross product are obtained.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.181-193
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• 2016

During the past two decades or so, fractional integral inequalities have proved to be one of the most powerful and far-reaching tools for the development of many branches of pure and applied mathematics. Very recently, many authors have presented some generalized inequalities involving the fractional integral operators. Here, using the pathway fractional integral operator, we give some presumably new and potentially useful fractional integral inequalities whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville type fractional integral operators. Relevant connections of the results presented here with those earlier ones are also pointed out.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.55-65
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• 2014

A graph G is called a fractional (g, f, n)-critical graph if any n vertices are removed from G, then the resulting graph admits a fractional (g, f)-factor. In this paper, we determine the new toughness condition for fractional (g, f, n)-critical graphs. It is proved that G is fractional (g, f, n)-critical if $t(G){\geq}\frac{b^2-1+bn}{a}$. This bound is sharp in some sense. Furthermore, the best toughness condition for fractional (a, b, n)-critical graphs is given.

• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.1
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• pp.81-86
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• 2016

Three hundred years ago, the fractional differential equation that is one of concept of fractional calculus released. Now, many researchers continue to try best effort applying into the control engineering, mathematics and physics. In this paper, the dynamics equation which is represented by Van der Pol, represent integer order and fractional order that having real order. Then this paper performs the comparisons between integer and real order as time series and phase portrait according to variation of parameter value for real order.

• East Asian mathematical journal
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• v.34 no.3
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• pp.249-263
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• 2018

We aim to establish certain Gronwall type inequalities associated with Riemann-Liouville k- and Hadamard k-fractional derivatives. The results presented here are sure to be new and potentially useful, in particular, in analyzing dependence solutions of certain k-fractional differential equations of arbitrary real order with initial conditions. Some interesting special cases of our main results are also considered.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.229-241
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• 2007

Multi-term fractional differential equations have been used to simulate fractional-order control system. It has been demonstrated the necessity of the such controllers for the more efficient control of fractional-order dynamical system. In this paper, the multi-term fractional ordinary differential equations are transferred into equivalent a system of equations. The existence and uniqueness of the new system are proved. A fractional order difference approximation is constructed by a decoupled technique and fractional-order numerical techniques. The consistence, convergence and stability of the numerical approximation are proved. Finally, some numerical results are presented to demonstrate that the numerical approximation is a computationally efficient method. The new method can be applied to solve the fractional-order control system.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.869-878
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• 2016

This paper presents an ecient fractional shifted Legendre polynomial method to solve the fractional Volterra's model for population growth model. The fractional derivatives are described based on the Caputo sense by using Riemann-Liouville fractional integral operator. The theoretical analysis, such as convergence analysis and error bound for the proposed technique has been demonstrated. In applications, the reliability of the technique is demonstrated by the error function based on the accuracy of the approximate solution. The numerical applications have provided the eciency of the method with dierent coecients of the population growth model. Finally, the obtained results reveal that the proposed technique is very convenient and quite accurate to such considered problems.

• Wind and Structures
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• v.28 no.6
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• pp.347-354
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• 2019

This study provides an approximate analytical solution to the fractional vibration problem of thin plate governing anomalous motion of plate subjected to in-plane loads. The method of variable separable is employed to transform the fractional partial differential equations under consideration into a fractional ordinary differential equation in temporal variable and a bi-harmonic plate equation in spatial variable. The technique of conformable fractional derivative is utilized to solve the resulting fractional differential equation and the approach of finite sine integral transform method is used to solve the accompanying bi-harmonic plate equation. The deflection field which measures the transverse displacement of the plate is expressed in terms of product of Bessel and trigonometric functions via the temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem of thin plate in literature. This work shows that conformable fractional derivative is an efficient mathematical tool for tracking analytical solution of fractional partial differential equation governing anomalous vibration of thin plates.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.16 no.12
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• pp.2716-2724
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• 2012

In this paper, a Phase Difference-to-Voltage Converter (PDVC) has been introduced into a conventional fractional-N PLL to suppress fractional spurs. The PDVC controls charge pump current depending on the phase difference of two input signals to phase frequency detector. The charge pump current decreases as the phase difference of two input signals increase. It results in the reduction of fractional spurs in the proposed fractional-N PLL. The proposed fractional-N PLL with PDVC has been designed based on a 1.8V $0.18{\mu}m$ CMOS process and proved by HSPICE simulation.