• Nonlinear Functional Analysis and Applications
• /
• v.29 no.1
• /
• pp.83-98
• /
• 2024

In this paper, we investigate the existence and uniqueness of solutions to a new class of integro-differential equation boundary value problems (BVPs) with ㄒ-Hilfer operator. Our problem is converted into an equivalent fixed-point problem by introducing an operator whose fixed points coincide with the solutions to the given problem. Using Banach's and Schauder's fixed point techniques, the uniqueness and existence result for the given problem are demonstrated. The stability results for solutions of the given problem are also discussed. In the end. One example is provided to demonstrate the obtained results

• Journal of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.803-829
• /
• 1998

We give general fixed point theorems for compact multimaps in the "better" admissible class $B^{K}$ defined on admissible convex subsets (in the sense of Klee) of a topological vector space not necessarily locally convex. Those theorems are used to obtain results for $\Phi$-condensing maps. Our new theorems subsume more than seventy known or possible particular forms, and generalize them in terms of the involving spaces and the multimaps as well. Further topics closely related to our new theorems are discussed and some related problems are given in the last section.n.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.1065-1092
• /
• 2018

This manuscript is involved with a category of second-order impulsive functional integro-differential equations with nonlocal conditions in Banach spaces. Sufficient conditions for existence and approximate controllability of mild solutions are acquired by making use of the theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem. An illustration is additionally furnished to prove the attained principles.

• Journal of applied mathematics & informatics
• /
• v.19 no.1_2
• /
• pp.261-280
• /
• 2005

We study the existence and nonexistence of positive periodic solutions of a non-autonomous functional differential equation with impulses. The equations we study may be of delay, advance or mixed type functional differential equations and the impulses may cause the existence of positive periodic solutions. The methods employed are fixed-point index theorem, Leray-Schauder degree, and upper and lower solutions. The results obtained are new, and some examples are given to illustrate our main results.

• Korean Journal of Mathematics
• /
• v.27 no.1
• /
• pp.119-129
• /
• 2019

Balance function is one of the joint factors to determine fall in risk theory. It helps to moderate the progression and riskiness of falls for detecting balance and fall risk factors. Nevertheless, the objective measures for balance function require expensive equipment with the assessment of any expertise. We establish the existence and uniqueness of a multi-order fractional differential equations based on ${\psi}$-Hilfer operator on time scales with balance function. This class describes the dynamic of time scales derivative. Our tool is based on the Schauder fixed point theorem. Here, sufficient conditions for Ulam-stability are given.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.32 no.3
• /
• pp.280-289
• /
• 2008

This paper presents design of the quantitative feedback control system of the three axes hydraulic road simulator with respect to the dummy wheel for uncertain multiple input-output(MIMO) feedback systems. This simulator has the uncertain parameters such as fluid compressibility, fluid leakage, electrical servo components and nonlinear mechanical connections. This works have reproduced the random input signal to implement the real road vibration's data in the lab. The replaced $m^2$ MISO equivalent control systems satisfied the design specifications of the original $m^*m$ MIMO control system and developed the mathematical method using quantitative feedback theory based on schauder's fixed point theorem. This control system illustrates a tracking performance of the closed-loop controller with low order transfer function G(s) and pre-filter F(s) having the minimum bandwidth for parameters of uncertain plant. The efficacy of the designed controller is verified through the dynamic simulation with combined hydraulic model and Adams simulator model. The Matlab simulation results to connect with Adams simulator model show that the proposed control technique works well under uncertain hydraulic plant system. The designed control system has satisfied robust performance with stability bounds, tracking bounds and disturbance. The Hydraulic road simulator consists of the specimen, hydraulic pump, servo valve, hydraulic actuator and its control equipments