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Stability Analysis of Linear Uncertain Differential Equations

  • Chen, Xiaowei;Gao, Jinwu
    • Industrial Engineering and Management Systems
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    • v.12 no.1
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    • pp.2-8
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    • 2013
  • Uncertainty theory is a branch of mathematics based on normolity, duality, subadditivity and product axioms. Uncertain process is a sequence of uncertain variables indexed by time. Canonical Liu process is an uncertain process with stationary and independent increments. And the increments follow normal uncertainty distributions. Uncertain differential equation is a type of differential equation driven by the canonical Liu process. Stability analysis on uncertain differential equation is to investigate the qualitative properties, which is significant both in theory and application for uncertain differential equations. This paper aims to study stability properties of linear uncertain differential equations. First, the stability concepts are introduced. And then, several sufficient and necessary conditions of stability for linear uncertain differential equations are proposed. Besides, some examples are discussed.

Exact Controllability for Fuzzy Differential Equations in Credibility Space

  • Lee, Bu Young;Youm, Hae Eun;Kim, Jeong Soon
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.14 no.2
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    • pp.145-153
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    • 2014
  • With reasonable control selections on the space of functions, various application models can take the shape of a well-defined control system on mathematics. In the credibility space, controlability management of fuzzy differential equation is as much important issue as stability. This paper addresses exact controllability for fuzzy differential equations in the credibility space in the perspective of Liu process. This is an extension of the controllability results of Park et al. (Controllability for the semilinear fuzzy integro-differential equations with nonlocal conditions) to fuzzy differential equations driven by Liu process.

A Dynamic Analysis of Constrained Multibody Systems (구속된 다물체 시스템을 위한 동역학 해석론)

  • 이상호;한창수;서문석
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.18 no.9
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    • pp.2339-2348
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    • 1994
  • The objective of this paper is to develop a solution method for the differential-algebraic equation(DAE) derived from constrained muti-body dynamic systems. Mechanical systems are often modeled as bodies and joints. Differential equations of motion are formulated for bodies. Since the bodies are connected by joint, the differential variables must satisfy the kinematic constraint equations that come from the joints. Difficulties are arised due to drift of the differential variables off the constraint equations. An optimization method is adopted to correct the drift of the differential variables. To demonstrate the efficiency of the proposed method a slider-crank mechanism is analyzed dynamically. Identical results are obtained as these from the commercial program DADS. Dynamic analysis of a High Mobility Multi-purpose Wheeled. Vehicle(HMMWV) is carried out to show the practicalism of the proposed method.

GENERALIZATION OF A FIRST ORDER NON-LINEAR COMPLEX ELLIPTIC SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS IN SOBOLEV SPACE

  • MAMOURIAN, A.;TAGHIZADEH, N.
    • Honam Mathematical Journal
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    • v.24 no.1
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    • pp.67-73
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    • 2002
  • In this paper we discuss on the existence of general solution of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z})+G(z,\;w,\;\bar{w})$ in the Sololev Space $W_{1,p}(D)$, that is generalization of a first order Non-linear Elliptic System of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$

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EXISTENCE OF EXTREMAL SOLUTIONS FOR FUZZY DIFFERENTIAL EQUATIONS DRIVEN BY LIU PROCESS

  • KWUN, YOUNG CHEL;KIM, JEONG SOON;PARK, YOUNG IL;PARK, JIN HAN
    • Journal of applied mathematics & informatics
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    • v.39 no.3_4
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    • pp.507-527
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    • 2021
  • In this paper, we study existence of extremal solutions for fuzzy differential equations driven by Liu process. To show extremal solutions, we define partial ordering relative to fuzzy process. This is an extension of the results of Kwun et al. [5] and Rodríguez-López [13] to fuzzy differential equations in credibility space.

GROWTH OF SOLUTIONS OF LINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS WITH COEFFICIENTS HAVING THE SAME LOGARITHMIC ORDER

  • Biswas, Nityagopal
    • Korean Journal of Mathematics
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    • v.29 no.3
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    • pp.473-481
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    • 2021
  • In this paper, we investigate the relations between the growth of meromorphic coefficients and that of meromorphic solutions of complex linear differential-difference equations with meromorphic coefficients of finite logarithmic order. Our results can be viewed as the generalization for both the cases of complex linear differential equations and complex linear difference equations.

EXISTENCE AND UNIQUENESS RESULTS FOR SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH INITIAL TIME DIFFERENCE

  • Nanware, J.A.;Dawkar, B.D.;Panchal, M.S.
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.5
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    • pp.1035-1044
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    • 2021
  • Existence and uniqueness results for solutions of system of Riemann-Liouville (R-L) fractional differential equations with initial time difference are obtained. Monotone technique is developed to obtain existence and uniqueness of solutions of system of R-L fractional differential equations with initial time difference.

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.

SOME OPIAL-TYPE INEQUALITIES APPLICABLE TO DIFFERENTIAL EQUATIONS INVOLVING IMPULSES

  • KIM, YOUNG JIN
    • The Pure and Applied Mathematics
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    • v.22 no.4
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    • pp.315-331
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    • 2015
  • The purpose of this paper is to obtain Opial-type inequalities that are useful to study various qualitative properties of certain differential equations involving impulses. After we obtain some Opial-type inequalities, we apply our results to certain differential equations involving impulses.

OSCILATION AND STABILITY OF NONLINEAR NEUTRAL IMPULSIVE DELAY DIFFERENTIAL EQUATIONS

  • Duan, Yongrui;Tian, Peng;Zhang, Shunian
    • Journal of applied mathematics & informatics
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    • v.11 no.1_2
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    • pp.243-253
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    • 2003
  • In this paper, oscillation and stability of nonlinear neutral impulsive delay differential equation are studied. The main result of this paper is that oscillation and stability of nonlinear impulsive neutral delay differential equations are equivalent to oscillation and stability of corresponding nonimpulsive neutral delay differential equations. At last, two examples are given to illustrate the importance of this study.