ISSN: 2456-8686, Volume 1, Issue 2, 2017:72-78 DOI : http://doi.org/10.26524/cm17 Some Integral Theorems Based on Generalized Difference Operator and its Equation Maria Susai Manuel M 1 , Gerly TG 2* and Dominic Babu G 3 1 Department of Science and Humanities, RMD Engineering College, Kavaraipettai, Chennai, Tamil Nadu, S.India. 2 Department of Mathematics, Sacred Heart College, Tirupattur, Vellore District, Tamil Nadu, S.India. 3 Department of Mathematics, Annai Velankanni College, Tholayavattam, Kanyakumari Dist.,Tamil Nadu, S.India. Abstract In this paper, we establish convolution theorem, discrete Fourier transform, discrete Green’s and Gauss Divergence theorems using a generalized difference operator and its equation. Also we present few examples verified by MATLAB to illustrate the theorems. Key words: Generalized difference equation, Convolution Theorem, Green’s Theorem, Divergence theorem. AMS Subject classification: 39A70, 47B39, 39A10, 49M. 1. Introduction Fractional calculus and fractional difference equations have undergone expanded study in recent years as a considerable interest both in Mathematics and in applications. They were applied in modeling of many physical and chemical processes and in engineering [1, 5, 6, 2]. The theory of generalized difference operator Δ ℓ defined as Δ ℓ v(k)= v(k + ℓ) − v(k) is developed in [3]. So in this paper, we extend the theory of Δ ℓ to the calculus of real functions for finding the values of some integral theorems using the inverse of generalized difference operator Δ ℓ . We complete this introduction with a brief description of the paper. This paper has five sections. In Section 2, we present some preliminary results. In Section 3, we derive convolution theorem for discrete Fourier transform for the sequence of real numbers. In section 4, we present the discrete Green’s theorem and Gauss Divergent theorem. 2* tgp.gerlyjose@yahoo.com Page 72 of 78