Solutions of fractional difference equations using S-transforms

J. Jagan Mohana,* and G.V.S.R. Deekshitulub

Solutions of fractional difference equations using S-transforms

Authors :

J. Jagan Mohan^a,* and G.V.S.R. Deekshitulu^b

Author Address :

^aFluid Dynamics Division, School of Advanced Sciences, VIT University, Vellore - 632014, Tamil Nadu, India.
^bDepartment of Mathematics, JNTU Kakinada, Kakinada - 533003, Andhra Pradesh, India.

*Corresponding author.

Abstract :

In the present paper, we define the nabla discrete Sumudu transform (S-transform) and present some of its basic properties. We obtain the nabla discrete Sumudu transform of fractional sums and di.erences. We apply this transform to solve some fractional di.erence equations with initial value problems. Finally, using S-transforms, we prove that discrete Mittag-Leffler function is the eigen function of Caputo type fractional di.erence operator $\Detla^\alpha$.

Keywords :

Difference equation, fractional di.erence, Caputo type, initial value problem, Sumudu transform.

DOI :

Article Info :

Received : February 09, 2013; Accepted : April 25, 2013.