Fractional fourier transform in the framework of fractional calculus operators

摘要

The paper is devoted to the study of a fractional Fourier transform in a special space of functions by Lizorkin. Connections of such a transform with differentiation operators are established and an inverse operator for such a transform if constructed. Compositions of the fractional Fourier transform with modified fractional integrals and derivatives are proved. Application to solution of a partial diffusion-type differential equation of fractional order is given.