Journal Article•

# The generalized convolutions with a weight function for laplace transform

TL;DR: In this paper, the authors introduce several new generalized convolutions with a weight function for the Laplace, Fourier sine and Fourier cosine integral transforms for solving a class of integral equations.

Abstract: In this paper, we introduce several new generalized convolutions with a weight function for the Laplace, Fourier sine and Fourier cosine integral transforms. Convolution properties and their applications for solving a class of integral equations and systems of integral equations are presented.

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TL;DR: In this article, the Kontorovich-Lebedev, Fourier sine, and Fourier cosine integral transforms are solved in closed form for a class of Fredholm integral equations with non-degenerate kernels.

Abstract: In this article, we solve in closed form a class of Fredholm integral equations and systems of Fredholm integral equations with nondegenerate kernels by using techniques of convolutions and generalized convolutions related to the Kontorovich-Lebedev, Fourier sine, and Fourier cosine integral transforms.

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01 Dec 2016TL;DR: In this paper, the generalized convolution with a weight function for the Hartley and Fourier cosine transforms is introduced, and several algebraic properties and applications of this generalized convolutions to solving a class of integral equations of Toeplitz plus Hankel type and a general class of systems of integral equation are presented.

Abstract: In this paper, we introduce the generalized convolution with a weight function for the Hartley and Fourier cosine transforms. Several algebraic properties and applications of this generalized convolution to solving a class of integral equations of Toeplitz plus Hankel type and a class of systems of integral equations are presented.