• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.139-153
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• 2021

In this paper, we study the existence of positive solutions for a class of conformable fractional differential equations with integral boundary conditions. By using the properties of Green's function with the fixed point theorem in a cone, we prove the existence of a positive solution. We also provide some examples to illustrate our results.

• Kyungpook Mathematical Journal
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• 제57권4호
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• pp.651-665
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• 2017

Some computational fluid dynamics problems concerning the thin films flow of viscous fluid with a free surface and draining or coating fluid-flow problems can be delineated by third-order ordinary differential equations. In this paper, the aim is to introduce the numerical solutions of the boundary value problems of such equations by variational iteration method. In this paper, it is shown that the third-order boundary value problems can be written as a system of integral equations, which can be solved by using the variational iteration method. These solutions are gleaned in terms of convergent series. Numerical examples are given to depict the method and their convergence.

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

• Korean Journal of Mathematics
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• 제29권2호
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• pp.227-237
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• 2021

Opial inequality and its consequences are useful in establishing existence and uniqueness of solutions of initial and boundary value problems for differential and difference equations. In this paper we analyze Opial-type inequalities for convex functions. We have studied different versions of these inequalities for a generalized integral operator. Further difference of Opial-type inequalities are utilized to obtain generalized mean value theorems, which further produce various interesting derivations for fractional and conformable integral operators.

• 대한조선학회논문집
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• 제43권6호
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• pp.683-692
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• 2006

The BEM, known as solving boundary value problems, could have some advantages In solving domain problems which are mostly solved by FEM and FDM. Lately, in the elastic-plastic nonlinear problems, BEM could provide the subdomain approach for the region where the plastic deformation could occur and the unknown nodal displacement of this region are added as the unknown of the boundary integral equation for this approach. In this paper, initial stress method was used to establish the formulation of such BEM approach. And a simple rectangular plate having a circular hole was analyzed to verify the suggested method and the result is compared with that from FEM. It is shown that the result of two methods are showing similar stress-strain curves at the root of perforated plate and furthermore the plastic deformation obtained by BEM shows more reasonable behavior than that of FEM.

• 대한수학회보
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• 제55권3호
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• pp.899-911
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• 2018

In this paper, we consider the second-order nonlinear differential equation with the nonlocal boundary conditions. We first reformulate this boundary value problem as a fixed point problem for a Fredholm integral equation operator, and then present a result on the existence and uniqueness of the solution by using the contraction mapping theorem. Furthermore, we establish a sufficient condition on the functions ${\mu}$ and $h_i$, i = 1, 2 that guarantee a unique solution for this nonlocal problem in a Hilbert space. Also, accurate analytic solutions in series forms for this boundary value problems are obtained by the Adomian decomposition method (ADM).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제1권1호
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• pp.29-33
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• 1994

There are various aspects of the solution of boundary-value problems for second-order linear elliptic equations in two independent variables. One useful method of solving such boundary-value problems for Laplace's equation is by means of suitable integral representations of solutions and these representations are obtained most directly in terms of particular singular solutions, termed Green's functions.(omitted)

• Structural Engineering and Mechanics
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• 제15권5호
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• pp.535-550
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• 2003

In this paper, a boundary-type meshfree method, the boundary radial point interpolation method (BRPIM), is presented for solving boundary value problems of two-dimensional solid mechanics. In the BRPIM, the boundary of a problem domain is represented by a set of properly scattered nodes. A technique is proposed to construct shape functions using radial functions as basis functions. The shape functions so formulated are proven to possess both delta function property and partitions of unity property. Boundary conditions can be easily implemented as in the conventional Boundary Element Method (BEM). The Boundary Integral Equation (BIE) for 2-D elastostatics is discretized using the radial basis point interpolation. Some important parameters on the performance of the BRPIM are investigated thoroughly. Validity and efficiency of the present BRPIM are demonstrated through a number of numerical examples.

• East Asian mathematical journal
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• 제27권3호
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• pp.319-337
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• 2011

We approximate a locally unique solution of a nonlinear equation in a Banach space setting using an inexact two-step Newton-type method. It turn out that under our new idea of recurrent functions, our semilocal analysis provides tighter error bounds than before, and in many interesting cases, weaker sufficient convergence conditions. Applications including the solution of nonlinear Chandrasekhar-type integral equations appearing in radiative transfer and two point boundary value problems are also provided in this study.

• 대한수학회지
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• 제38권2호
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• pp.365-383
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• 2001

We consider path integrals, more precisely projective systems of Fresnel distributions, associated with Sturm-Liouville boundary value problems.