We present here generalized Canavati type -fractional Polya type inequalities. We cover also the iterated case. Our inequalities are with respect to all norms:
. We finish with applications.
You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.
References
[1] G.A. Anastassiou, Fractional Differentiation Inequalities, Research Monograph,
Springer, New York, 2009.
[2] G.A. Anastassiou, On right fractional calculus, Chaos, Solitons and Fractals,
42 (2009), 365-376.
[3] G.A. Anastassiou, Inteligent Mathematics: Computational Analysis,
Springer, Heidelberg, 2011.
[4] G.A. Anastassiou, Intelligent Comparisons: Analytic Inequalities,
Springer, Heidelberg - New York, 2016.
[5] G.A. Anastassiou, Generalized Canavati type fractional Taylor’s formulae,
J. Computational Analysis and Applications, 21, No 7 (2016), 1205-1212.
[6] J.A. Canavati, The Riemann-Liouville integral, Nieuw Archief Voor
Wiskunde, 5, No 1 (1987), 53-75.
[7] A.M.A. El-Sayed, M. Gaber, On the finite Caputo and finite Riesz derivatives,
Electronic J. of Theoretical Physics, 3, No 12 (2006), 81-95.
[8] G.S. Frederico, D.F.M. Torres, Fractional optimal control in the sense of
Caputo and the fractional Noether’s theorem, Internat. Math. Forum, 3,
No 10 (2008), 479-493.
[9] R. Gorenflo, F. Mainardi, Essentials of Fractional Calculus, 2000, Maphysto
Center,
http://www.maphysto.dk/oldpages/events/LevyCAC2000/
MainardiNotes/fm2k0a.ps.
[11] G. Polya, Ein mittelwertsats f¨ur Funktionen mehrerer Ver¨anderlichen, Tohoku
Math. J., 19 (1921), 1-3.
[12] G. Polya and G. Szeg¨o, Aufgaben und Lehrs¨artze aus der Analysis, Volume
I, Springer-Verlag, Berlin, 1925 (In German).
[13] G. Polya and G. Szeg¨o, Problems and Theorems in Analysis, Volume I,
Classics in Mathematics, Springer-Verlag, Berlin, 1972.
[14] G. Polya and G. Szeg¨o, Problems and Theorems in Analysis, Volume I,
Chinese Edition, 1984.
[15] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives,
Theory and Applications, Gordon and Breach, Amsterdam, 1993
[English transl. from the Russian, Integrals and Derivatives of Fractional
Order and Some of Their Applications, Nauka i Tekhnika, Minsk, 1987].
880 G.A. Anastassiou
[16] E.T. Whittaker and G.N. Watson, A Course in Modern Analysis, Cambridge
University Press, 1927.