Le Xuan Huy

Bio: Le Xuan Huy is an academic researcher. The author has contributed to research in topics: Sine and cosine transforms & Two-sided Laplace transform. The author has an hindex of 2, co-authored 4 publications receiving 8 citations.

The Fourier–Laplace Generalized Convolutions and Applications to Integral Equations

Abstract: In this paper we introduce two generalized convolutions for the Fourier cosine, Fourier sine and Laplace integral transforms. Convolution properties and their applications to solving integral equations and systems of integral equations are considered.

On the Fourier–Laplace convolution transforms

Abstract: In this paper, we introduce two classes of integral transforms related to two generalized convolutions for the Fourier cosine, Fourier sine and Laplace transforms. The Watson type theorem for these transforms is also obtained. As applications we apply these convolutions to solve some classes of integral and integro-differential equations.

The generalized convolutions with a weight function for laplace transform

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.

Fourier cosine-Laplace generalized convolution inequalities and applications

Abstract: We introduce several weighted Lp(R+) -norm inequalities and integral transform related to the generalized convolution with a weight function for the Fourier cosine and Laplace transforms. Some applications of these inequalities to estimate the solutions of some partial differential equations are considered. We also obtained solutions of a class of the Toeplitz plus Hankel integro-differential equations in closed form. Mathematics subject classification (2010): 33C10, 44A35, 45E10, 45J05, 47A30, 47B15.

Integral transforms and their applications

Abstract: Integral transforms (Laplace, Fourier and Mellin) are introduced with their properties, the relationship between these transforms was discussed and some important applications in physics and engineering were given. ااااااا دقل مت ضارعتسإ ةساردو ل ةيلماكتلا تليوحتلا لك ، سلبل تلوحت نم روف ي ر نيليمو عم ةشقانم كلذكو ،اهنم لك صاوخ و صئاصخ ةقلعلا ةشقانم مت هذه نيب طبرلاو و ،تليوحتلا مت ميدقت تاقيبطتلا ضعب تليوحتلا هذهل ةمهملا يف تلاجم ءايزيفلا ةسدنهلاو.

A class of Fredholm equations and systems of equations related to the Kontorovich-Lebedev and the Fourier integral transforms

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.

Fourier cosine-Laplace generalized convolution inequalities and applications

Abstract: We introduce several weighted Lp(R+) -norm inequalities and integral transform related to the generalized convolution with a weight function for the Fourier cosine and Laplace transforms. Some applications of these inequalities to estimate the solutions of some partial differential equations are considered. We also obtained solutions of a class of the Toeplitz plus Hankel integro-differential equations in closed form. Mathematics subject classification (2010): 33C10, 44A35, 45E10, 45J05, 47A30, 47B15.

The explicit solutions for a class of fractional Fourier–Laplace convolution equations

Abstract: In this paper, two types of fractional Fourier–Laplace convolutions are defined, and the corresponding fractional Fourier–Laplace convolution theorems associated with the fractional cosine transform (FRCT), fractional sine transform (FRST) and Laplace transform (LP) are investigated in detail. The relationship between the fractional Fourier–Laplace convolutions and the existing convolutions is given, and Young's type theorem as well as the weighted convolution inequality are also obtained. As an application for fractional Fourier–Laplace convolution, the filter design and the system of convolution-type integral equations are also considered, the computational complexity for the multiplicative filter is analysed, and explicit solutions for these equations are obtained.