Different type kernel h−fractional differences and their fractional h−sums

By Thabet Abdeljawad. Chaos, Solitons & Fractals, 2018

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Abstract The aim of this article is to recall and study fractional derivatives with singular kernels on h Z and define fractional derivatives with non-singular exponential and Mittag–Leffler kernels on h Z and study some of their properties. We shall follow the nabla time scale analysis and relate the h − nabla classical discrete fractional derivatives to the delta existing ones studied before by some authors. Some dual identities between left and right and delta and nabla, left and right h − fractional difference types will be investigated. The nabla h − discrete versions of the Mittag-Leffler functions will be recalled by means of the nabla h − fatorial functions and nabla h − Taylor polynomials. The discrete Laplace on h Z and its convolution theory are used often to proceed in our investigation. The obtained results will generalize the nabla classical discrete fractional differences and the nabla discrete fractional differences with discrete exponential and M L − kernels studied recently by Abdeljawad and Baleanu by setting h = 1 .

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/cca004145f4400edc19c29f2bfd8927e0c81452d