Principles of Delta and Nabla Fractional Differences

Details Principles of Delta and Nabla Fractional Differences Principles of Delta and Nabla Fractional Differences

2011-12-25

arxiv.org/abs/1112.5795v1

Mathematics

Dynamical Systems

Scientific paper

We define nabla right fractional sum and difference and obtain a nabla integration by parts formula. Some properties of nabla and delta fractional sums and differences are obtained to derive dual identities between the nabla and delta ones and other $\mathbb{Q}$-dual identities to relate left and right ones. These dual identities give the impression that the definition of the delta right fractional difference presented by Abdeljawad and Baleanu in \cite{Th Caputo} and \cite{TDbyparts} are more appropriate than those introduced by other authors. Hence, the delta integration by parts formula formulated in \cite{TDbyparts} and the nabla one presented in this article are consistent.

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