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Zbl 1198.26033
Anastassiou, George A.
Foundations of nabla fractional calculus on time scales and inequalities. (English)
[J] Comput. Math. Appl. 59, No. 12, 3750-3762 (2010). ISSN 0898-1221

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 $\bbfR$, $\bbfZ$.
MSC 2000:
*26E70
26A33 Fractional derivatives and integrals (real functions)

Keywords: fractional calculus on time scales; nabla Poincaré inequality; nabla Sobolev inequality; nabla Opial inequalities; nabla Ostrowski inequality; nabla Hilbert-Pachpatte inequality; fractional inequalities

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