• Journal of Applied and Pure Mathematics
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• 제4권3_4호
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• pp.107-122
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• 2022

This manuscript aims to investigate the existence, uniqueness, and stability of non-local random impulsive neutral stochastic differential time delay equations (NRINSDEs) with Poisson jumps. First, we prove the existence of mild solutions to this equation using the Banach fixed point theorem. Next, we demonstrate the stability via continuous dependence initial value. Our study extends the work of Wang, and Wu [16] where the time delay is addressed by the prescribed phase space 𝓑 (defined in Section 3). To illustrate the theory, we also provide an example of our methods. Using our results, one could investigate the controllability of random impulsive neutral stochastic differential equations with finite/infinite states. Moreover, one could extend this study to analyze the controllability of fractional-order of NRINSDEs with Poisson jumps as well.

• 대한수학회논문집
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• 제38권3호
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• pp.967-982
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• 2023

The goal of this study is to derive a class of random impulsive non-local fractional stochastic differential equations with finite delay that are of Caputo-type. Through certain constraints, the existence of the mild solution of the aforementioned system are acquired by Kransnoselskii's fixed point theorem. Furthermore through Ito isometry and Gronwall's inequality, the Hyers-Ulam stability of the reckoned system is evaluated using Lipschitz condition.

• 충청수학회지
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• 제29권1호
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• pp.83-93
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• 2016

In this paper, we introduce a generalized quadratic functional equation with several variables and then investigate its generalized Hyers-Ulam stability in normed spaces.

• 충청수학회지
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• 제33권2호
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• pp.205-217
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• 2020

We will introduce a new type of quartic functional equation and then investigate the stability for a quartic functional equation in a convex modular space.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.373-388
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• 2010

We introduce mixed cubic-quartic functional equations. And using the fixed point method, we prove the generalized Hyers-Ulam stability of cubic-quartic functional equations on random normed spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권1호
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• pp.15-26
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• 2021

The purpose of this paper is to introduce a new type of a cubic functional equation and then investigate its stability problems in a convex modular space with a generalized ∆a-condition.

• 충청수학회지
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• 제23권3호
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• pp.411-424
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• 2010

In this paper we consider a generalized form of quadratic functional equations and establish new theorems about the generalized Hyers-Ulam stability of the generalized form of quadratic equations in fuzzy normed spaces.

• 한국세라믹학회지
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• 제33권1호
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• pp.110-118
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• 1996

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2004년도 추계학술대회 논문집
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• pp.1148-1153
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• 2004

This paper presents the mechanism to increase lateral stability of a mobile robot using an energy stability margin theory. Previous measure of stability used in a wheeled mobile robot has been based on a static stability margin. However, the static stability margin is independent of the height of the robot and does not provide sufficient measure for the amount of stability when the terrain is not a horizontal plane. In this work, the energy stability margin theory, which is dependent on robot's height is used to develop a 2 dof mechanism to increase lateral stability. This proposed mechanism shifts the center of gravity of the robot to the point where the energy stability margin is maximized and overall stability of the robot equipped with this mechanism will be increased.

• Journal of Electrical Engineering and Technology
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• 제8권6호
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• pp.1530-1541
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• 2013

The coexistence and extinction of species are important concepts for biological systems and can be distinguished by an investigation of stability. When determining local stability of nonlinear systems, Lyapunov indirect method based on the Jacobian linearization has been widely employed due to its simplicity. Despite such popularity, it is not applicable to singular systems whose Jacobian has at least one eigenvalue that is equal to zero. In such singular cases, an appropriate Lyapunov function should be sought to determine the stability of systems, which is rather difficult and quite involved. In this paper, we seek for a simple criterion to determine stability of the equilibrium that is located at the boundary of the positive orthant, when one of eigenvalues of the Jacobian is zero. The goal of the paper is to present a generalized condition for the equilibrium to attract all trajectories that starting from initial condition in the positive orthant and near the equilibrium. Unlike the Lyapunov direct method, the proposed method requires just a simple algebraic computation for checking the stability of the critical point. Our approach is applied to various biological systems to show the effectiveness of the proposed method.