- Research Article
- Open Access
Fractional Quantum Integral Inequalities
© H. Öğünmez and U. M. Özkan. 2011
- Received: 10 November 2010
- Accepted: 16 February 2011
- Published: 10 March 2011
- Positive Integer
- Real Number
- Exponential Function
- Specific Time
- Similar Calculation
The study of fractional -calculus in  serves as a bridge between the fractional -calculus in the literature and the fractional -calculus on a time scale , where , and .
In this paper, we have obtained fractional -integral inequalities, which are quantum versions of inequalities (1.1), (1.2), and (1.3), on the specific time scale , where , and . In general, a time scale is an arbitrary nonempty closed subset of the real numbers .
In this section, we will state our main results and give their proofs.
and the proof is complete.
The following result may be seen as a generalization of Theorem 3.1.
We prove this theorem by induction.
and this ends the proof.
The authors thank referees for suggestions which have improved the final version of this paper.
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