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Foundations of nabla fractional calculus on time scales and inequalities. (English) Zbl 1198.26033

Summary: Here we develop the nabla fractional calculus on time scales. Then we produce related integral inequalities of types: Poincaré, Sobolev, Opial, Ostrowski and Hilbert-Pachpatte. Finally we give inequality applications on the time scales \(\mathbb{R}\), \(\mathbb{Z}\).

MSC:

26E70 Real analysis on time scales or measure chains
26A33 Fractional derivatives and integrals
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