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.

Keywords:

• convolution
• Fourier sine transform
• Fourier cosine transform
• Laplace transform
• integral equation
• integro-differential equation

2010 Mathematics Subject Classification:

• 33C10
• 44A35
• 45E10
• 45J05
• 47A30
• 47B15

Acknowledgments

The authors sincerely thank the referee for his constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This research is funded by Vietnam's National Foundation for Science and Technology Development (NAFOSTED) [grant number 101.02-2014.08].