New bounds for the Ostrowski-type inequalities via conformable fractional calculus

  • Fuat Usta
  • Hüseyin Budak
  • Tuba Tunç
  • Mehmet Zeki Sarikaya
Open Access


In this paper, we have introduced the new upper bounds for Ostrowski-type integral inequalities by using conformable fractional integral. In accordance with this purpose, we have benefited from the Taylor expansion for conformable fractional derivatives which was introduced by Anderson.

Mathematics Subject Classification

26D15 26A33 41A58 41A55 65D30 



  1. 1.
    Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Abdeljawad, T.; Alzabut, J.; Jarad, F.: A generalized Lyapunov-type inequality in the frame of conformable derivatives. Adv. Differ. Equ. 2017, 321 (2017). MathSciNetCrossRefGoogle Scholar
  3. 3.
    Anderson, D.R.: Taylor’s formula and integral inequalities for conformable fractional derivatives. In: Pardalos, P.M., Rassias, T.M. (eds.) Contributions in Mathematics and Engineering, pp. 25–43. Springer, Switzerland (2016)CrossRefGoogle Scholar
  4. 4.
    Anderson, D.R.; Ulness, D.J.: Results for conformable differential equations (2016) (preprint) Google Scholar
  5. 5.
    Atangana, A.; Baleanu, D.; Alsaedi, A.: New properties of conformable derivative. Open Math. 13, 889–898 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Hammad, M.A.; Khalil, R.: Conformable fractional heat differential equations. Int. J. Differ. Equ. Appl. 13, 177–183 (2014)zbMATHGoogle Scholar
  7. 7.
    Hammad, M.A.; Khalil, R.: Abel’s formula and Wronskian for conformable fractional differential equations. Int. J. Differ. Equ. Appl. 13, 177–183 (2014)zbMATHGoogle Scholar
  8. 8.
    Huy, V.N.; Ngo, Q.A.: New bounds for the Ostrowski-like type inequalities. Bull. Korean Math. Soc. 48, 95–104 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Iyiola, O.S.; Nwaeze, E.R.: Some new results on the new conformable fractional calculus with application using D’Alambert approach. Progr. Fract. Differ. Appl. 2, 115–122 (2016)CrossRefGoogle Scholar
  10. 10.
    Katugampola, U.: A new fractional derivative with classical properties. arXiv:1410.6535v2
  11. 11.
    Khalil, R.; Al Horani, M.; Yousef, A.; Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Kilbas, A.A.; Srivastava, H.M.; Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier B.V, Amsterdam (2006)zbMATHGoogle Scholar
  13. 13.
    Ostrowski, A.M.: Über die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert. Comment. Math. Helv. 10, 226–227 (1938)CrossRefzbMATHGoogle Scholar
  14. 14.
    Samko, S.G.; Kilbas, A.A.; Marichev, O.I.: Fractional Integrals and Derivatives: Theory and Applications. Gordonand Breach, Yverdon et alibi (1993)zbMATHGoogle Scholar
  15. 15.
    Sarikaya, M.Z.: Gronwall type inequality for conformable fractional integrals. Konuralp J. Math. 4(2), 217–222 (2016)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Usta, F.; Sarikaya, M.Z.: On generalization conformable fractional integral inequalities (2016) (preprint) Google Scholar
  17. 17.
    Sarikaya, M.Z.; Usta, F.: On comparison theorems for conformable fractional differential equations. Int. J. Anal. Appl. 12(2), 207–214 (2016)zbMATHGoogle Scholar
  18. 18.
    Sarikaya, M.Z.; Budak, H.: New inequalities of Opial type for conformable fractional integrals. Turk. J. Math. 41(5), 1164–1173 (2017)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Usta, F.; Sarikaya, M.Z.: Explicit bounds on certain integral inequalities via conformable fractional calculus. Cogent Math. 4(1), 1277505 (2017). MathSciNetCrossRefGoogle Scholar
  20. 20.
    Zheng, A.; Feng, Y.; Wang, W.: The Hyers-Ulam stability of the conformable fractional differential equation. Math. Aeterna 5(3), 485–492 (2015)Google Scholar
  21. 21.
    Al-Rifae, M.; Abdeljawad, T.: Fundamental results of conformable SturmLiouville eigenvalue problems, Complexity, vol. 2017, Article ID 3720471.
  22. 22.
    Katugampola, U.N.: New approach to generalized fractional integral. Appl. Math. Comput. 218, 860–865 (2011)MathSciNetzbMATHGoogle Scholar
  23. 23.
    Jarad, F.; Uurlu, E.; Abdeljawad, T.; Baleanu, D.: On a new class of fractional operators. Adv. Differ. Equ. 2017, 247 (2017)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Anderson, D.R.; Ulness, D.J.: Newly defined conformable derivatives. Adv. Dyn. Syst. Appl. 10(2), 109–137 (2015)MathSciNetGoogle Scholar

Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Fuat Usta
    • 1
  • Hüseyin Budak
    • 1
  • Tuba Tunç
    • 1
  • Mehmet Zeki Sarikaya
    • 1
  1. 1.Department of Mathematics, Faculty of Science and ArtsDüzce UniversityDüzceTurkey

Personalised recommendations