• Title/Summary/Keyword: Differential equation

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A DIFFERENTIAL EQUATION FOR MULTIPLE BESSEL POLYNOMIALS WITH RAISING AND LOWERING OPERATORS

  • Baek, Jin-Ok;Lee, Dong-Won
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.3
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    • pp.445-454
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    • 2011
  • In this paper, we first find a raising operator and a lowering operator for multiple Bessel polynomials and then give a differential equation having multiple Bessel polynomials as solutions. Thus the differential equations were found for all multiple orthogonal polynomials that are orthogonal with respect to the same type of classical weights introduced by Aptekarev et al.

ON FUZZY STOCHASTIC DIFFERENTIAL EQUATIONS

  • KIM JAI HEUI
    • Journal of the Korean Mathematical Society
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    • v.42 no.1
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    • pp.153-169
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    • 2005
  • A fuzzy stochastic differential equation contains a fuzzy valued diffusion term which is defined by stochastic integral of a fuzzy process with respect to 1-dimensional Brownian motion. We prove the existence and uniqueness of the solution for fuzzy stochastic differential equation under suitable Lipschitz condition. To do this we prove and use the maximal inequality for fuzzy stochastic integrals. The results are illustrated by an example.

THE APPLICATION OF STOCHASTIC DIFFERENTIAL EQUATIONS TO POPULATION GENETIC MODEL

  • Choi, Won;Choi, Dug-Hwan
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.4
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    • pp.677-683
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    • 2003
  • In multi-allelic model $X\;=\;(x_1,\;x_2,\;\cdots\;,\;x_d),\;M_f(t)\;=\;f(p(t))\;-\;{\int_0}^t\;Lf(p(t))ds$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we examine the stochastic differential equation for model X and find the properties using stochastic differential equation.

ON THE GALERKIN-WAVELET METHOD FOR HIGHER ORDER DIFFERENTIAL EQUATIONS

  • Fukuda, Naohiro;Kinoshita, Tamotu;Kubo, Takayuki
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.3
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    • pp.963-982
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    • 2013
  • The Galerkin method has been developed mainly for 2nd order differential equations. To get numerical solutions, there are some choices of Riesz bases for the approximation subspace $V_j{\subset}L^2$. In this paper we shall propose a uniform approach to find suitable Riesz bases for higher order differential equations. Especially for the beam equation (4-th order equation), we also report numerical results.

FRACTIONAL GREEN FUNCTION FOR LINEAR TIME-FRACTIONAL INHOMOGENEOUS PARTIAL DIFFERENTIAL EQUATIONS IN FLUID MECHANICS

  • Momani, Shaher;Odibat, Zaid M.
    • Journal of applied mathematics & informatics
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    • v.24 no.1_2
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    • pp.167-178
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    • 2007
  • This paper deals with the solutions of linear inhomogeneous time-fractional partial differential equations in applied mathematics and fluid mechanics. The fractional derivatives are described in the Caputo sense. The fractional Green function method is used to obtain solutions for time-fractional wave equation, linearized time-fractional Burgers equation, and linear time-fractional KdV equation. The new approach introduces a promising tool for solving fractional partial differential equations.

A NOTE ON THE APPROXIMATE SOLUTIONS TO STOCHASTIC DIFFERENTIAL DELAY EQUATION

  • KIM, YOUNG-HO;PARK, CHAN-HO;BAE, MUN-JIN
    • Journal of applied mathematics & informatics
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    • v.34 no.5_6
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    • pp.421-434
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    • 2016
  • The main aim of this paper is to discuss the difference between the Euler-Maruyama's approximate solutions and the accurate solution to stochastic differential delay equation. To make the theory more understandable, we impose the non-uniform Lipschitz condition and weakened linear growth condition. Furthermore, we give the pth moment continuous of the approximate solution for the delay equation.

ANTI-PERIODIC SOLUTIONS FOR HIGHER-ORDER LIÉENARD TYPE DIFFERENTIAL EQUATION WITH p-LAPLACIAN OPERATOR

  • Chen, Taiyong;Liu, Wenbin
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.3
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    • pp.455-463
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    • 2012
  • In this paper, by using degree theory, we consider a kind of higher-order Li$\acute{e}$enard type $p$-Laplacian differential equation as follows $$({\phi}_p(x^{(m)}))^{(m)}+f(x)x^{\prime}+g(t,x)=e(t)$$. Some new results on the existence of anti-periodic solutions for above equation are obtained.

SEMILINEAR NONLOCAL DIFFERENTIAL EQUATIONS WITH DELAY TERMS

  • Jeong, Jin-Mun;Cheon, Su Jin
    • Journal of the Korean Mathematical Society
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    • v.50 no.3
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    • pp.627-639
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    • 2013
  • The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder's fixed point theorem. We construct the fundamental solution, establish the H$\ddot{o}$lder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions of the given equation.