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COMMUNICATIONS 115 Math. Commun
The main goal of this paper is to study properties of the fractional Fourier transform on Schwartz type space S θ. Symbol class S m,θ ρ,σ is introduced. The fractional pseudo-differential operators (f.p.d.o.) associated with the symbol a(x, ξ) are a continuous linear mapping of S into S θ. Kernel and integral representations of f.p.d.o are obtained. The boundedness property of f.p.d.o. is studied. Application of the fractional Fourier transform in solving a generalized Fredholm integral equation is also given.fatcat:eupyhviyzvaw5ji5oojqcgkvce