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Anastassiou, George A.

Principles of delta fractional calculus on time scales and inequalities. (English) Zbl 1201.26001

Math. Comput. Modelling 52, No. 3-4, 556-566 (2010).
Summary: Here we develop the Delta Fractional Calculus on Time Scales. Then we produce related integral inequalities of types: Poincaré, Sobolev, Opial, Ostrowski and Hilbert-Pachpatte. Finally, we give inequalities’ applications on the time scale \(\mathbb{R}\).

Cited in 43 Documents

MSC:

26A33 Fractional derivatives and integrals
26D15 Inequalities for sums, series and integrals
26E70 Real analysis on time scales or measure chains

Keywords:

fractional calculus on time scales; delta Poincaré inequality; delta Sobolev inequality; delta Opial inequality; delta Ostrowski inequality; delta Hilbert-Pachpatte inequality
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\textit{G. A. Anastassiou}, Math. Comput. Modelling 52, No. 3--4, 556--566 (2010; Zbl 1201.26001)
Full Text: DOI

References:

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