New Integral Transform in Caputo Type Fractional Difference Operator

In this paper, we introduce Caputo type nabla ( ,ℎ) −fractional difference operators and investigate their basic properties and also to show the applicability of this interesting ( ,ℎ) −new integral transform method and its efficiency in solving linear fractional difference equations. Differential equations with fractional derivative provide a natural framework for the discussion of various kinds of real problems modeled by the aid of fractional derivative. Discrete analogues of some topics of continuous fractional calculus have been developed. Finally, we provide the general solutions in terms of discrete Mittag− Leffler functions.