41 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 © Global Society of Scientific Research and Researchers http://asrjetsjournal.org/ On the Relationship Between the Fractional Sumudu Transform and Fractional Fourier Transform Sadaf Saeed a , Saleem Iqbal b *, Farhana Sarwar c , Abdul Rehman d a,b,d Department of Mathematics, University of Balochistan, Quetta 87300, Pakistan c Department of Mathematics F.G.Girls Degree College, Madrissa Road, Quetta, Cantt, 87300, Pakistan a Email: sadafimran6zg@gmail.com b Email: saleemiqbal81@yahoo.com c Email: f_saleem10@yahoo.com c Email: rehman_maths@hotmail.com Abstract In this paper we have discussed the kernel of fractional Sumudu transforms and its relationship with fractional Fourier transform which will play a significant role for fractional Sumudu transform to recognize its importance like other fractional transforms. Keywords: Sumudu Transform; Fractional Sumudu transform; Fractional Laplace Transform; Fractional Mellin Transform; Fractional Fourier Transform. 1. Introduction The Sumudu transform which is introduced in 1993[1] is not as well-known as other transforms like Laplace, Fourier, Mellin, Hilbert and other transforms. Sumudu transform carries some advantages as compare to other transform and it is found capable in solving complicated problems. The fundamental properties of Sumudu transform were established in [2] and subsequently applied to partial differential equations [3-5]. The Sumudu transform which is equivalent to the Laplace transform also leads to a series of properties in a similar way like Laplace transform. The Sumudu transform may be used to solve problems without resorting to a new frequency domain [6-7]. ------------------------------------------------------------------------ * Corresponding author.