Open AccessFractional convolution associated with a class of integral equations
Author(s) -
Feng Qiang,
Wang RongBo
Publication year - 2020
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
eISSN - 1751-9683
pISSN - 1751-9675
DOI - 10.1049/iet-spr.2019.0140
Subject(s) - convolution (computer science) , convolution theorem , mathematics , convolution power , sine , integral transform , integral equation , class (philosophy) , fractional calculus , circular convolution , type (biology) , overlap–add method , mathematical analysis , fractional fourier transform , fourier transform , computer science , geometry , fourier analysis , artificial intelligence , ecology , artificial neural network , biology
Three kinds of generalised convolution operations of fractional cosine transform and fractional sine transform are investigated, and the corresponding convolution theorems are derived, which can be seen as the generalisation of the classical results. The relationships of these generalised fractional convolution operations are also discussed. Additionally, the potential applications of the derived results in solving two kinds of generalised convolution integral equations are discussed, and the explicit solutions of these convolution‐type integral equations are obtained.