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

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.407-420
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• 2023

In this manuscript, we study the sufficient conditions for controllability of Volterra-Fredholm type fractional integro-differential systems in a Banach space. Fractional calculus and the fixed point theorem are used to derive the findings. Some examples are provided to illustrate the obtained results.

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

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.113-130
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• 2024

In this work, we explore the existence and uniqueness results for a class of boundary value issues for implicit Volterra-Fredholm nonlinear integro-differential equations (IDEs) with Atangana-Baleanu-Riemann fractional (ABR-fractional) that have non-instantaneous multi-point fractional boundary conditions. The findings are supported by Krasnoselskii's fixed point theorem, Gronwall-Bellman inequality, and the Banach contraction principle. Finally, a demonstrative example is provided to support our key findings.

• Composites Research
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• 제16권5호
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• pp.21-27
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• 2003

선형 압전 이론(theory of linear piezoelectricity)을 이용하여 면외전단 충격(anti-plane shear impact)을 받는 기능경사 압전 세라믹(functionally graded piezoelectric ceramic)의 중앙에 존재하는 균열(central crack)의 동적 응답에 대해 연구한다. 기능경사 압전재료의 물성치(material property)는 두께방향을 따라 연속적으로 변한다고 가정한다. 라플라스 변환(Laplace transform)과 푸리에 변환(Fourier transform)을 사용하여 두 쌍의 복합적분 방정식을 구성하며, 이를 제2종 Fredholm 적분 방정식(Fredholm integral equations of the second kind)으로 표현한다. 재료 물성치의 변화도(gradient of material properties)와 전기하중(electric loading)의 영향을 보기 위해 동응력세기계수(dynamic stress intensity factor)에 대한 수치 결과를 제시하였다.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.137-162
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• 2024

This paper consists of two significant aims. The first aim of this paper is to establish the criteria for the existence of solutions to nonlinear Volterra-Fredholm (V-F) fractional integral equations on [0, L], where 0 < L < ∞. The fractional integral is described here in the sense of the Katugampola fractional integral of order λ > 0 and with the parameter β > 0. The concepts of the fixed point theorem and the measure of noncompactness are used as the main tools to prove the existence of solutions. The second aim of this paper is to introduce a computational method to obtain approximate numerical solutions to the considered problem. This method is based on the Fibonacci wavelets with collocation technique. Besides, the results of the error analysis and discussions of the accuracy of the solutions are also presented. To the best knowledge of the authors, this is the first computational method for this generalized problem to obtain approximate solutions. Finally, two examples are discussed with the computational tables and convergence graphs to interpret the efficiency and applicability of the presented method.

• 대한수학회논문집
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• 제7권2호
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• pp.307-311
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• 1992

• 대한수학회지
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• 제9권2호
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• pp.85-89
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• 1972

• 한국수학교육학회지시리즈A:수학교육
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• 제14권1호
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• pp.27-27
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• 1975

• 한국수학교육학회지시리즈A:수학교육
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• 제21권2호
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• pp.7-10
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• 1983