• Kyungpook Mathematical Journal
• /
• 제53권2호
• /
• pp.257-271
• /
• 2013

In this article, we establish the existence of at least three unbounded positive solutions to a boundary-value problem of the nonlinear singular fractional differential equation. Our analysis relies on the well known fixed point theorems in the cones.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제21권3호
• /
• pp.195-206
• /
• 2014

In this paper, we consider, under a hybrid iterative scheme with errors, a weak convergence theorem to a common element of the set of a finite family of asymptotically k-strictly pseudo-contractive mappings and a solution set of an equilibrium problem for a given bifunction, which is the approximation version of the corresponding results of Kumam et al.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제25권1호
• /
• pp.16-25
• /
• 2021

This paper is studied the existence of a solution for the impulsive Cauchy problem involving the Caputo fractional derivative in Banach space by using topological structures. We based on using topological degree method and fixed point theorem with some suitable conditions. Further, some topological properties for the set of solutions are considered. Finally, an example is presented to demonstrate our results.

• 대한수학회지
• /
• 제35권3호
• /
• pp.727-740
• /
• 1998

Controlling traffic lights at a bottleneck, in [5] a time of open passage is called optimal, if it minimizes the first moment of the asymptotic distribution of the queue length. The discussion of the first moment as function of the time of open passage is based on an analysis of the behavior of a fixed point when varying control parameters and delivers theoretical and computational aspects of the traffic problem.

• Nonlinear Functional Analysis and Applications
• /
• 제28권3호
• /
• pp.851-863
• /
• 2023

We study the appropriate conditions for the findings of uniqueness and existence for a group of boundary value problems for impulsive Ψ-Caputo fractional nonlinear Volterra-Fredholm integro-differential equations (V-FIDEs) with symmetric boundary non-instantaneous conditions in this paper. The findings are based on the fixed point theorem of Krasnoselskii and the Banach contraction principle. Finally, the application is provided to validate our primary findings.

• Journal of applied mathematics & informatics
• /
• 제40권1_2호
• /
• pp.305-316
• /
• 2022

We study the existence and uniqueness of solutions for a class of boundary value problems of nonlinear fractional order differential equations involving the Caputo fractional derivative by employing the Banach's contraction principle and the Schauder's fixed point theorem. In addition, an example is given to demonstrate the application of our main results.

• Nonlinear Functional Analysis and Applications
• /
• 제29권1호
• /
• pp.165-177
• /
• 2024

In this paper, we investigate the suitable conditions for the existence results for a class of 𝔍-Hilfer fractional nonlinear Fredholm-Volterra models with new conditions. The findings are based on Banach contraction principle and Schauder's fixed point theorem. Also, the generalized Hyers-Ulam stability and generalized Hyers-Ulam-Rassias stability for solutions of the given problem are provided.

• Nonlinear Functional Analysis and Applications
• /
• 제29권2호
• /
• pp.545-558
• /
• 2024

In this study, a class of nonlinear boundary fractional Caputo Volterra-Fredholm integro-differential equations (CV-FIDEs) is taken into account. Under specific assumptions about the available data, we firstly demonstrate the existence and uniqueness features of the solution. The Gronwall's inequality, a adequate singular Hölder's inequality, and the fixed point theorem using an a priori estimate procedure. Finally, a case study is provided to highlight the findings.

• Nuclear Engineering and Technology
• /
• 제54권2호
• /
• pp.532-545
• /
• 2022

In-depth convergence analyses for neutronics/thermal-hydraulics (T/H) coupled calculations are performed to investigate the performance of nonlinear methods based on the Fixed-Point Iteration (FPI). A simplified neutronics-T/H coupled system consisting of a single fuel pin is derived to provide a testbed. The xenon equilibrium model is considered to investigate its impact during the nonlinear iteration. A problem set is organized to have a thousand different fuel temperature coefficients (FTC) and moderator temperature coefficients (MTC). The problem set is solved by the Jacobi and Gauss-Seidel (G-S) type FPI. The relaxation scheme and the Anderson acceleration are applied to improve the convergence rate of FPI. The performances of solution schemes are evaluated by comparing the number of iterations and the error reduction behavior. From those numerical investigations, it is demonstrated that the number of FPIs is increased as the feedback is stronger regardless of its sign. In addition, the Jacobi type FPIs generally shows a slower convergence rate than the G-S type FPI. It also turns out that the xenon equilibrium model can cause numerical instability for certain conditions. Lastly, it is figured out that the Anderson acceleration can effectively improve the convergence behaviors of FPI, compared to the conventional relaxation scheme.

• Journal of the Optical Society of Korea
• /
• 제20권5호
• /
• pp.633-640
• /
• 2016

In a dual lens stereoscopic camera, a convergence point determines the stereopsis effects of a video. When a user zooms an object, a convergence point is fixed since it is not coupled with a zoom function. Due to the fixed convergence point, it is possible for a zoom to cause the excessive binocular disparity resulting in visual discomfort. In this paper, to solve this problem, we build the relational model including all phenomena possible to arise and propose the adjustment methods of a convergence point by the positions of a focus, an object and a convergence point. We also evaluate the experiments measuring a binocular disparity and the subjective test to investigate the visual comfort. The results show that one of the proposed methods produced more comfortable 3D images to viewers than the others.