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Conformable fractional integral inequalities of Chebyshev type

  • Erhan Set
  • İlker Mumcu
  • Sevdenur Demirbaş
Original Paper
  • 3 Downloads

Abstract

A number of Chebyshev type inequalities involving various fractional integral operators have, recently, been presented. Here, motivated essentially by the earlier works and their applications in diverse research subjects, we aim to establish several Chebyshev type inequalities involving generalized new conformable fractional integral operator.

Keywords

Riemann–Liouville fractional integral operators New conformable fractional integral operators Chebyshev inequality 

Mathematics Subject Classification

26A33 26D10 33B20 

Notes

References

  1. 1.
    Belarbi, S., Dahmani, Z.: On some new fractional integral inequalities. J. Inequalities Pure Appl. Math. 10(3), 5 (2009)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Chebyshev, P.L.: Sur les expressions approximatives des integrales definies par les autres prises entre les mmes limites. Proc. Math. Soc. Charkov 2, 93–98 (1882)Google Scholar
  3. 3.
    Chen, F.: Extensions of the Hermite–Hadamard inequality for convex functions via fractional integrals. J. Math. Inequalities 10(1), 75–81 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Dahmani, Z.: New inequalities in fractional integrals. Int. J. Nonlinear Sci. 9(4), 493–497 (2010)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Gorenflo, R., Mainardi, F.: Fractional Calculus: Integral and Differential Equations of Fractional Order, pp. 223–276. Springer, Vienna (1997)Google Scholar
  6. 6.
    İşcan, İ.: Hermite–Hadamard–Fejér type inequalities for convex functions via fractional integrals. Stud. Univ. Babe-Bolyai Math. 60(3), 355–366 (2015)zbMATHGoogle Scholar
  7. 7.
    Jarad, F., Uǧurlu, E., Abdeljawad, T., Baleanu, D.: On a new class of fractional operators. Adv. Differ. Equ. 2017(1), 247 (2017).  https://doi.org/10.1186/s13662-017-1306-z MathSciNetCrossRefGoogle Scholar
  8. 8.
    Katugampola, U.N.: New approach to a genaralized fractional integral. Appl. Math. Comput. 218(3), 860–865 (2011)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Kilbas, A.A.: Hadamard-type fractional calculus. J. Korean Math. Soc. 38(6), 1191–1204 (2001)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematical Studies, vol. 204. Elsevier (North-Holland) Science Publishers, Amsterdam (2006)Google Scholar
  11. 11.
    Machado, J.T., Kiryakova, V., Mainardi, F.: Recent history of fractional calculus. Commun. Nonlinear Sci. Numer. Simul. 16, 1140–1153 (2011)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Özdemir, M.E., Set, E., Akdemir, A.O., Sarkaya, M.Z.: Some new Chebyshev type inequalities for functions whose derivatives belongs to \(L_{p}\) spaces. Afrika Matematika 26, 1609–1619 (2015)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Podlubny, I.: Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications. Academic Press, San Diego (1999)zbMATHGoogle Scholar
  14. 14.
    Sarıkaya, M.Z., Set, E., Yaldız, H., Başak, N.: Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities. Math. Comput. Model. 57(9), 2403–2407 (2013)CrossRefGoogle Scholar
  15. 15.
    Set, E.: New inequalities of Ostrowski type for mappings whose derivatives are \(s\)-convex in the second sense via fractional integrals. Comput. Math. Appl. 63(7), 1147–1154 (2012)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Set, E., İşcan, İ., Zehir, F.: On some new inequalities of Hermite–Hadamard type involving harmonically convex functions via fractional integrals. Konuralp J. Math. 3(1), 42–55 (2015)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Set, E., Dahmani, Z., Mumcu, I.: New extensions of Chebyshev type inequalities using generalized Katugampola integrals via Pólya–Szeg inequality. IJOCTA 8(2), 137–144 (2018)MathSciNetGoogle Scholar

Copyright information

© The Royal Academy of Sciences, Madrid 2018

Authors and Affiliations

  1. 1.Department of MathematicsFaculty of Science and Arts, Ordu UniversityOrduTurkey

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