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Cubo (Temuco)

versão On-line ISSN 0719-0646

Cubo vol.14 no.1 Temuco  2012

http://dx.doi.org/10.4067/S0719-06462012000100001 

CUBO A Mathematical Journal Vol.14, N° 01, (01-07). March 2012

 

Univariate right fractional Ostrowski inequalities

George A. Anastassiou

University of Memphis, Department of Mathematical Sciences, Memphis, TN 38152, U.S.A. email: ganastss@memphis.edu


ABSTRACT

Very general univariate right Caputo fractional Ostrowski inequalities are presented. One of them is proved sharp and attained. Estimates are with respect to

 

Keywords and Phrases: Ostrowski inequality, right Caputo fractional derivative.

2010 AMS Mathematics Subject Classication: 26A33, 26D10, 26D15


RESUMEN

Se presenta de manera muy general desigualdades univariadas derechas de Caputo fraccionarias de Ostrowski. Se prueba que una de ellas es aguda Las estimaciones con respecto a


 

References

[1] G.A. Anastassiou, Ostrowski type inequalities, Proc. AMS 123 (1995), 3775-3781.

[2] G.A. Anastassiou, Fractional Differentiation Inequalities, Research Monograph, Springer, New York, 2009.

[3] G.A. Anastassiou, On Right Fractional Calculus, Chaos, Solitons and Fractals, 42 (2009), 365- 376.

[4] A.M.A. El-Sayed, M. Gaber, On the finite Caputo and finite Riesz derivatives, Electronic Journal of Theoretical Physics, Vol. 3, No. 12 (2006), 81-95.

[5] G.S. Frederico, D.F.M. Torres, Fractional Optimal Control in the sense of Caputo and the fractional Noether's theorem, International Mathematical Forum, Vol. 3, No. 10 (2008), 479- 493.

[6] R. Gorenflo, F. Mainardi, Essentials of Fractional Calculus, 2000, Maphysto Center, http://www.maphysto.dk/oldpages/events/LevyCAC2000/ MainardiNotes/fm2k0a.ps.

[7] A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funcktion von ihrem Integralmittelwert, Comment. Math. Helv., 10 (1938), 226-227.

[8] 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)].


Received: November 2010. Revised: March 2011.