The explicit solutions for a class of fractional Fourier–Laplace convolution equations. Issue 2 (1st February 2023)

• Record Type: Journal Article
• Authors: Feng, Q.; Yuan, S.
• Is Part Of: Integral transforms and special functions. Volume 34:Issue 2(2023)
• Page Start: 128
• Page End: 144
• Publication Date: 2023-02-01
• Subjects: Fractional Fourier transform -- Laplace transform -- convolution theorem -- filter -- convolution equation; 44A35 -- 45E10 -- 47A30; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2022.2093870
• Languages: English
• ISSNs: 1065-2469

Abstract

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.