• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.833-846
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• 1999

In this paper, we will study the relationship between the controlling factor of the solution to a difference equation and the solution of the corresponding differential equation. Many times the controlling factors are the same. But even the controlling factor of the two solutions may be different, we will discover a way to compute, for first order non-linear equations, the controlling factor of the solution to the difference equation using the solution of the differential equation.

• The Pure and Applied Mathematics
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• v.24 no.3
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• pp.147-153
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• 2017

In this paper, we propose a numerical method to solve fuzzy differential equations. Numerical experiments show that when the step size is small, the new method has significantly good approximate solutions of fuzzy differential equation. Graphical representation of fuzzy solutions in three-dimension is also provided as a reference of visual convergence of the solution sequence.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.65-77
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• 2006

By using general means, some oscillation criteria for second order nonlinear elliptic differential equation with damping $$\sum_{i,j=1}^{N}D_i[a_{ij}(x)D_iy]+\sum_{i=1}^{N}b_i(x)D_iy+p(x)f(y)=0$$ are obtained. These criteria are of a high degree of generality and extend the oscillation theorems for second order linear ordinary differential equations due to Kamenev, Philos and Wong.

• Kyungpook Mathematical Journal
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• v.21 no.1
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• pp.71-74
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• 1981

In this paper a general third order differential equation encountered in the flow of fluids in general and hopefully elsewhere. Sufficient conditions for existence & uniqueness of its solutions are given.

• Journal of the Korean Institute of Telematics and Electronics
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• v.16 no.5
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• pp.18-26
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• 1979

This paper extends some well-known system theories on algebraic matrix Lyapunov and Riccati equations. These extended results contain two point boundary conditions in matrix differential equations and include conventional results as special cases. Necessary and sufficient conditions are derived under which linear systems are stabilizable with feedback gains derived from periodic two-point boundary matrix differential equations. An iterative computation method for two-point boundary differential Riccati equations is given with an initial guess method. The results in this paper are related to periodic feedback controls and also to the quadratic cost problem with a discrete state penalty.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.449-471
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• 2023

In this paper, we study a linear system of homogeneous commensurate /incommensurate fractional-order differential equations by developing a new semi-analytical scheme. In particular, by decoupling the system into two fractional-order differential equations, so that the first equation of order (δ + γ), while the second equation depends on the solution for the first equation, we have solved the under consideration system, where 0 < δ, γ ≤ 1. With the help of using the Adomian decomposition method (ADM), we obtain the general solution. The efficiency of this method is verified by solving several numerical examples.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.295-309
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• 2020

In this paper we study the growth of solutions of some non-linear complex differential equations in connection to Brück conjecture using the theory of complex differential equation.

• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.47-52
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• 1996

We consider the third order linear homogeneous differential equation L$_3$(y) = y(equation omitted) ＋ P($\chi$)y' ＋ Q($\chi$)y = 0 (E) P($\chi$) $\geq$ 0, Q($\chi$) ＞ 0 and P($\chi$)/Q($\chi$) is nondecreasing on [${\alpha}$, $\infty$) for some real number ${\alpha}$. (1) In this paper we discuss the distribution of zeros of solutions and a condition of oscillatory for equation (E).(omitted)

• Computers and Concrete
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• v.23 no.5
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• pp.303-309
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• 2019

This study investigates axisymmetric fractional vibration of an isotropic hyperelastic semi-linear thin disc with a view to examine effects of finite deformation associated with the material of the disc and effects of fractional vibration associated with the motion of the disc. The generalized three-dimensional equation of motion is reduced to an equivalent time fraction one-dimensional vibration equation. Using the method of variable separable, the resulting equation is further decomposed into second-order ordinary differential equation in spatial variable and fractional differential equation in temporal variable. The obtained solution of the fractional vibration problem under consideration is described by product of one-parameter Mittag-Leffler and Bessel functions in temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem in literature. Finally, and amongst other things, the Cauchy's stress distribution in thin disc under finite deformation exhibits nonlinearity with respect to the displacement fields whereas in infinitesimal deformation hypothesis, these stresses exhibit linear relation with the displacement field.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.45 no.3
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• pp.399-406
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• 1996

This paper presents a method of hierarchical state estimation of the time-varying linear systems via Block-pulse function(BPF). When we estimate the state of the systems where noise is considered, it is very difficult to obtain the solutions because minimum error variance matrix having a form of matrix nonlinear differential equations is included in the filter gain calculation. Therefore, hierarchical approach is adapted to transpose matrix nonlinear differential equations to a sum of low order state space equation from and Block-pulse functions are used for solving each low order state space equation in the form of simple and recursive algebraic equation. We believe that presented methods are very attractive nd proper for state estimation of time-varying linear systems on account of its simplicity and computational convenience. (author). 13 refs., 10 figs.