On the Fourier–Laplace convolution transforms

In this paper, four types of fractional Fourier cosine and sine Laplace weighted convolutions are defined, and the corresponding fractional Fourier cosine and sine Laplace convolution theorems associated with the fractional cosine transform, fractional sine transform and Laplace transform are derived in detail. Furthermore, the relationship between the fractional Fourier cosine (sine) Laplace weighted convolutions and existing convolutions are studied, and Young's type theorem is also investigated. In addition, as an application for fractional Fourier cosine (sine)‐Laplace weighted convolution, the system of convolution‐type integral equations is considered, the computational complexity is analysed and the explicit solutions for these equations are obtained.

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

Feng

Yuan

2022

Integral Transforms and Special Functions

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On the Fourier–Laplace convolution transforms

Cited by 3 publications

References 6 publications

On a Polyconvolution with a Weight Function for Fourier Cosine and Laplace Transforms

On a Polyconvolution with a Weight Function for Fourier Cosine and Laplace Transforms

Fractional Fourier cosine and sine Laplace weighted convolution and its application

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

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