• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.165-177
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• 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
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• 제29권1호
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• pp.259-273
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• 2024

In this manuscript, we study the sufficient conditions for existence and uniqueness results of solutions of impulsive Hilfer fractional Volterra-Fredholm integro-differential equations with integral boundary conditions. Fractional calculus and Banach contraction theorem used to prove the uniqueness of results. Moreover, we also establish Hyers-Ulam stability for this problem. An example is also presented at the end.

• 대한수학회지
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• 제55권4호
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• pp.877-895
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• 2018

In this paper, we show that an unbounded $S_0$-demicompact linear operator T with respect to a bounded linear operator $S_0$, acting on a Banach space, can be characterized by the Kuratowskii measure of noncompactness. Moreover, some other quantities related to this measure provide sufficient conditions to the operator T to be $S_0$-demicompact. The obtained results are used to discuss the connection with Fredholm and upper Semi-Fredholm operators.

• 제어로봇시스템학회논문지
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• 제9권9호
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• pp.658-663
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• 2003

In deterministic design of feedback controllers for uncertain dynamic systems, the upper bound of the uncertainty is very important to guarantee the stability of the closed loop system. In this paper, we assume that the upper bound of the uncertainty is formulated using a Fredholm integral equation of the first kind, that is, an integral of the product of a predefined kernel with an unknown influence function. We propose an adaptation law that is capable of estimating this upper bound. Using this adaptive upper bound, we design an adaptive variable structure control (AVSC), which guarantees asymptotic stability/ultimate boundedness of uncertain dynamic systems. The illustrative example shows the proposed AVSC is effective for uncertain dynamic systems.

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.869-881
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• 2020

Most first kind integral equations are ill-posed, and obtaining their numerical solution often requires solving a linear system of algebraic equations of large condition number, which may be difficult or impossible. This article proposes a regularization-direct method to numerically solve first kind Fredholm integral equations. The vector forms of block-pulse functions and related properties are applied to formulate the direct method and reduce the integral equation to a linear system of algebraic equations. We include a regularization scheme to overcome the ill-posedness of integral equation and obtain a stable numerical solution. Some test problems are solved using the proposed regularization-direct method to illustrate its efficiency for solving first kind Fredholm integral equations.

• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.867-872
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• 1999

In this paper we study the stability theorems for nonlinear Fredholm-Volterra integral equations system.

• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.575-583
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• 2000

In this work, we solve the Fredholm-Volterra integral equation(FVIE) when the kernel takes a potential function form under given conditions. we represent this kernel in the Weber-sonin integral form.

• 대한수학회보
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• 제53권3호
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• pp.681-698
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• 2016

In this paper, we investigate relative essential spectra of $2{\times}2$ block operator matrix using the Fredholm perturbation theory. Furthermore, an example for two-group transport equations is presented to illustrate the validity of the main results.

• 대한수학회보
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• 제43권3호
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• pp.653-655
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• 2006

We give a simple proof of the statement that if T is a bounded linear operator on a complex HIlbert space then T is Fredholm if and only if ${\pi}(T)$ is not a TDZ, where ${\pi}(\cdot)$ is the Catkin homomorphism.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.223-236
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• 2000

In this paper, we solve the Fredholm integral equation of the first and second kind when the kernel takes a singular form. Also, some important relations for Chebyshev polynomial of integration are established.