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Balanced Canavati Fractional Opial Inequalities

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 609))

Abstract

Here we present \(L_{p}\), \(p>1\), fractional Opial type inequalities subject to high order boundary conditions.

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References

  1. R.P. Agarwal, P.Y.H. Pang, Opial Inequalities with Applications in Differential and Difference Equations (Kluwer, Dordrecht, 1995)

    Book  Google Scholar 

  2. G.A. Anastassiou, Fractional Differentiation Inequalities, Research Monograph (Springer, New York, 2009)

    Book  Google Scholar 

  3. G.A. Anastassiou, On right fractional calculus. Chaos, Solitons Fractals 42, 365–376 (2009)

    Article  MathSciNet  Google Scholar 

  4. G.A. Anastassiou, Balanced Canavati type fractional opial inequalities. J. Appl. Func. Anal. 9(3-4), 230-238 (2014)

    Google Scholar 

  5. P.R. Beesack, On an integral inequality of Z. Opial. Trans. Am. Math. Soc. 104, 470–475 (1962)

    Article  MathSciNet  Google Scholar 

  6. J.A. Canavati, The Riemann-Liouville Integral. Nieuw Archief Voor Wiskunde 5(1), 53–75 (1987)

    MathSciNet  Google Scholar 

  7. A.M.A. El-Sayed, M. Gaber, On the finite Caputo and finite Riesz derivatives. Electron. J. Theor. Phys. 3(12), 81–95 (2006)

    Google Scholar 

  8. G.S. Frederico, D.F.M. Torres, Fractional optimal control in the sense of Caputo and the fractional Noether’s theorem. Int. Math. Forum 3(10), 479–493 (2008)

    MathSciNet  Google Scholar 

  9. R. Gorenflo, F. Mainardi, Essentials of fractional calculus (Maphysto Center, 2000), http://www.maphysto.dk/oldpages/events/LevyCAC2000/MainardiNotes/fm2k0a.ps

  10. C. Olech, A simple proof of a certain result of Z. Opial. Ann. Polon. Math. 8, 61–63 (1960)

    MathSciNet  Google Scholar 

  11. Z. Opial, Sur une inegalite. Ann. Polon. Math. 8, 29–32 (1960)

    MathSciNet  Google Scholar 

  12. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, (Gordon and Breach, Amsterdam, 1993) [English translation from the Russian, Integrals and Derivatives of Fractional Order and Some of Their Applications (Nauka i Tekhnika, Minsk, 1987)]

    Google Scholar 

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Correspondence to George A. Anastassiou .

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Anastassiou, G.A. (2016). Balanced Canavati Fractional Opial Inequalities. In: Intelligent Comparisons: Analytic Inequalities. Studies in Computational Intelligence, vol 609. Springer, Cham. https://doi.org/10.1007/978-3-319-21121-3_4

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  • DOI: https://doi.org/10.1007/978-3-319-21121-3_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21120-6

  • Online ISBN: 978-3-319-21121-3

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