Title: Some New Ostrowski Type Inequalities via Fractional Integrals
Author(s): Ghulam Farid
Pages: 64-68
Cite as:
Ghulam Farid, Some New Ostrowski Type Inequalities via Fractional Integrals, Int. J. Anal. Appl., 14 (1) (2017), 64-68.


We have found a new version of well known Ostrowski inequality in a very simple and antique way via Riemann-Liouville fractional integrals. Also some related results have been derived.

Full Text: PDF



  1. P. Cerone, S. S. Dragomir, Midpoint-type rules from an inequalities point of view, handbook of analytic-computational methods in applied mathematics, Editor: G. Anastassiou, CRC Press, New York, 2000.

  2. S. S. Dragomir, Ostrowski-type inequalities for Lebesgue integral: A survey of recent results, Aust. J. Math. Anal. Appl., 14 (1) (2017), 1-287.

  3. S. S. Dragomir, T. M. Rassias, (Eds.) Ostrowski-type inequalities and applications in numerical integration, Kluwer academic publishers, Dordrecht, Boston, London, 2002.

  4. S. S. Dragomir, S. Wang, An inequality of Ostrowski-Grüss type and its applications to the estimation of error bounds for some special means and some numerical quadrature rules, Comput. Math. Appl., 33 (1997), 15-20.

  5. G. Farid, Straightforward proofs of Ostrowski inequality and some related results, Int. J. Anal. 2016 (2016), Article ID 3918483.

  6. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, 204, Elsevier, New York-London, 2006.

  7. H. Laurent, Sur le calcul des derivees a indicies quelconques, Nouv. Annales de Mathematiques., 3 (3) (1884), 240-252.

  8. M. Lazarevi´ c, Advanced topics on applications of fractional calculus on control problems, System stability and modeling, WSEAS Press, 2014.

  9. A. V. Letnikov, Theory of differentiation with arbitray pointer (Russian), Matem. Sbornik., 3 (1868), 1-66.

  10. K. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, John, Wiley and sons Inc, New York, 1993.

  11. A. Ostrowski, Uber die Absolutabweichung einer dierentierbaren Funktion von ihren Integralmittelwert, Comment. Math. Helv., 10 (1938), 226-227.

  12. X. Qiaoling, Z. Jian, L. Wenjun, A new generalization of Ostrowski-type inequality involving functions of two independent variables, Comput. Math. Appl., 60 (2010), 2219–2224.

  13. N. Y. Sonin, On differentiation with arbitray index, Moscow Matem. Sbornik., 6 (1) (1869), 1-38.

  14. Z. Tomovski, R. Hiller, H. M. Srivastava, Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler function, Integral Transforms Spec. Funct., 21 (11) (2010), 797-814.