• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.709-717
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• 2005

Integral equations occur naturally in many fields of mechanics and mathematical physics. We consider the Fredholm integral equation of the first kind.In this paper we are interested in integral equation of convolution type. We give approximate solution by Meyer wavelets

• 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.

• Kyungpook Mathematical Journal
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• v.51 no.3
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• pp.251-260
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• 2011

The aim of this paper is to obtain a solution of a certain multidimensional convolution integral equation of Fredholm type whose kernel involves a generalized polynomial set. A number of results follow as special cases from the main theorem by specifying the parameters of the generalized polynomial set.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.593-601
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• 2022

Let C(Q) denote Yeh-Wiener space, the space of all real-valued continuous functions x(s, t) on Q ≡ [0, S] × [0, T] with x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. For each partition τ = τ_m,n = {(s_i, t_j)|i = 1, . . . , m, j = 1, . . . , n} of Q with 0 = s₀ < s₁ < . . . < s_m = S and 0 = t₀ < t₁ < . . . < t_n = T, define a random vector X_τ : C(Q) → ℝ^mn by X_τ (x) = (x(s₁, t₁), . . . , x(s_m, t_n)). In this paper we study the conditional integral transform and the conditional convolution product for a class of cylinder type functionals defined on K(Q) with a given conditioning function X_τ above, where K(Q)is the space of all complex valued continuous functions of two variables on Q which satify x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. In particular we derive a useful equation which allows to calculate the conditional integral transform of the conditional convolution product without ever actually calculating convolution product or conditional convolution product.

• Smart Structures and Systems
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• v.17 no.5
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• pp.753-771
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• 2016

This paper addresses the free and transient responses of a SDOF linear complex stiffness system by making use of the Hilbert transform and the convolution integral. Because the second-order differential equation of motion having the complex stiffness give rise to the conjugate complex eigen values, its time-domain analysis using the standard time integration scheme suffers from the numerical instability and divergence. In order to overcome this problem, the transient response of the linear complex stiffness system is obtained by the convolution integral of a green function which corresponds to the unit-impulse free vibration response of the complex system. The damped free vibration of the complex system is theoretically derived by making use of the state-space formulation and the Hilbert transform. The convolution integral is implemented by piecewise-linearly interpolating the external force and by superimposing the transient responses of discretized piecewise impulse forces. The numerical experiments are carried out to verify the proposed time-domain analysis method, and the correlation between the real and imaginary parts in the free and transient responses is also investigated.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.2
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• pp.125-136
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• 2018

In this article, a homotopy perturbation transform method (HPTM) and the Laplace transform combined with Taylor expansion method are presented for solving Volterra integral equations with a convolution kernel. The (HPTM) is innovative in Laplace transform algorithm and makes the calculation much simpler while in the Laplace transform and Taylor expansion method we first convert the integral equation to an algebraic equation using Laplace transform then we find its numerical inversion by power series. The numerical solution obtained by the proposed methods indicate that the approaches are easy computationally and its implementation very attractive. The methods are described and numerical examples are given to illustrate its accuracy and stability.

• Kyungpook Mathematical Journal
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• v.19 no.1
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• pp.135-139
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• 1979

We consider the problem that how must the production of certain item vary as a function of time, if for known losses due to depreciation the total amount of the product is to have a constant value. The integral equation associated with the problem is solved by an appeal to the convolution quotients. The production function comes out to be an expression containing the generalized Laguerre polynomials. The loss function and the production function are tabulated for different values of the parameter by using an IBM 370/145 computer.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.119-122
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• 1988

In recent years, several authors have dealt with the fraction derivative [1], in special functions [2], convolution integral equation [5], differintegral equation [4], the derivative of H-function [6], and some other applications. The present paper considers the fraction derivatve in the form of differential eqiation.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.49-58
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• 2010

In the present article we consider the diffusive Nicholson's blowflies equation with nonlocal delay incorporated into an integral convolution over all the past time and the whole infinite spatial domain $\mathbb{R}$. When the kernel function takes a special function, we construct a pair of lower and upper solutions of the corresponding travelling wave equation and obtain the existence of travelling fronts according to the existence result of travelling wave front solutions for reaction diffusion systems with nonlocal delays developed by Wang, Li and Ruan (J. Differential Equations, 222(2006), 185-232).

• Transactions of the Korean Society of Mechanical Engineers
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• v.8 no.6
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• pp.599-603
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• 1984

Field equations describing the effective behavior of general heterogeneous media are derived from the integral balance relations through the methods of distribution and convolution.