Fractional convolution associated with a class of integral equations

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.