Using this extension there are many results and application's obtained mainly by Alieva Tatiana in, , Almedia L.B.in, victor Namis in, Mcbride Kerr in and precisely the product and convolution theorems are derived by Ahmed Zayed in, L.B.Almeida in and Gaikwad and Chaudhary in etc. So a new convolution is defined for two functions in L 1 (R n ) ∩ C 1 (R n ), by using usual convolution and convolution in convolution and product theorem of one dimensional Fractional Fourier transform given by Ahmed Zayed in. Due to many applications of Fourier transform, in this paper the n-dimensional fractional Fourier transform which is defined in and its convolution are considered, n-dimensional fractional Fourier transform of usual product and convolution of two n-dimensional functions are obtained in but they are not in usual form as like convolution and product theorem of Fourier and Laplace transform.
We know that the one dimensional Fourier transform is extended to one dimensional Fractional Fourier transform.
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