• Honam Mathematical Journal
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• v.37 no.4
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• pp.397-409
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• 2015

This paper considers a class of new convolution integral equations whose kernels involve special functions such as the generalized Mittag-Leffler function and the extended Kummer hypergeometric function. Some basic properties of interconnection with the familiar Riemann-Liouville operators are obtained which are used in fiding the solution of the main convolution integral equation. Several consequences are deduced from the main result by incorporating certain extended forms of hypergeometric functions in our present investigation.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.163-174
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• 1999

The purpose of this paper is to obtain the solution of Fredholm-Volterra integral equation with singular kernel in the space $L_2(-1, 1)\times C(0,T), 0 \leq t \leq T< \infty$, under certain conditions,. The numerical method is used to solve the Fredholm integral equation of the second kind with weak singular kernel using the Toeplitz matrices. Also the error estimate is computed and some numerical examples are computed using the MathCad package.

• East Asian mathematical journal
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• v.34 no.5
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• pp.651-660
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• 2018

This paper concerned the existence of positive solutions to the second order differential systems with strongly coupled integral boundary value conditions. By using Krasnoselskii fixed point theorem, we prove the existence of positive solutions according to the parameters under the proper nonlinear growth conditions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.111-123
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• 2005

Here, the Fredholm integral equation with Hilbert kernel is solved numerically, using two different methods. Also the error, in each case, is estimated.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.253-260
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• 2002

In this paper, a good interpolation formulae are applied to the numerical solution of Cauchy integral equations of the first kind with using some Chebyshev quadrature rules. To demonstrate the effectiveness of the Radau-Chebyshev with respect to the olds, [6],[7],[8] and [121, some examples are given.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.7
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• pp.2167-2173
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• 1996

An approximate weight function technique using the indirect boundary integral equation has been presented for the analysis of stress intensity foactors(SIFs) of a thick pipe. One-term boundary integral was introduced to represent the crack surface displacement field for the displacement based weight function technique. An explicit closed-form SIF solution applicable to symmetric cracked pipes without any modification of the solution including both circumferential and radial cracks has been derived. The necessary information in the analysis is two or three reference SIFs. In most cases the SIF solution were in good agreement with those available in the literature.

• Steel and Composite Structures
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• v.23 no.3
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• pp.263-271
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• 2017

A theoretical study was carried-out of mode II delamination fracture behavior of the End Loaded Split (ELS) functionally graded beam configuration with considering the material non-linearity. The mechanical response of ELS was modeled analytically by using a power-law stress-strain relation. It was assumed that the material is functionally graded transversally to the beam. The non-linear fracture was investigated by using the J-integral approach. Equations were derived for the crack arm curvature and zero axes coordinate that are needed for the J-integral solution. The analysis developed is valid for a delamination crack located arbitrary along the beam height. The J-integral solution was verified by analyzing the strain energy release rate with considering material non-linearity. The effects of material gradient, non-linear material behavior and crack location on the fracture were evaluated. The solution derived is suitable for parametric analyses of non-linear fracture. The results obtained can be used for optimization of functionally graded beams with respect to their mode II fracture performance. Also, such simplified analytical models contribute for the understanding of delamination fracture in functionally graded beams exhibiting material non-linearity.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.35D no.12
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• pp.21-29
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• 1998

Dual integral equation in the spectral domain is derived for an arbitrary angled perfect conducting wedge with E-polarized plane wave incidence. Analytic integration of the dual integral equation in the spectral domain with the exact boundary fields of the perfect conducting wedge, the well known series solution, gives the exact asymptotic solution. The validity of the integration is assured by showing that analytic integration gives the null fields in the complementary region.

• Coupled systems mechanics
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• v.6 no.1
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• pp.97-111
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• 2017

The present paper reports an analytical study of delamination fracture in the Mixed Mode Flexure (MMF) functionally graded beam with considering the material non-linearity. The mechanical behavior of MMF beam is modeled by using a non-linear stress-strain relation. It is assumed that the material is functionally graded along the beam height. Fracture behavior is analyzed by the J-integral approach. Non-linear analytical solution is derived of the J-integral for a delamination located arbitrary along the beam height. The J-integral solution derived is verified by analyzing the strain energy release rate with considering the non-linear material behavior. The effects of material gradient, crack location along the beam height and material non-linearity on the fracture are evaluated. It is found that the J-integral value decreases with increasing the upper crack arm thickness. Concerning the influence of material gradient on the non-linear fracture, the analysis reveals that the J-integral value decreases with increasing the ratio of modulus of elasticity in the lower and upper edge of the beam. It is found also that non-linear material behavior leads to increase of the J-integral value. The present study contributes for the understanding of fracture in functionally graded beams that exhibit material non-linearity.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.609-621
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• 2013

At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.