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.View full textDownload full textKeywordsFourier and fractional Fourier transforms, modified Liouville fractional derivatives and integrals, operational relations, diffusion-type fractional differential equation, Laplace transform, Mittag-Leffler function 2000 MSC Subject Classification Codes 42A38, 26A33, 35A22, 35L15, 44A10, 47G10, 47B38, 33E12Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/10652461003676099