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Year 2019, Volume 9, Issue 4, 01.12.2019

Abstract

References

  • [1] Abdeljawad, T., (2015), On conformable fractional calculus, J. Comput. Appl. Math., 279, pp. 57-66.
  • [2] Dahmani, Z., Tabharit, L. and Taf, S., (2010), New Generalization of Gr¨uss inequality using RiemannLiouville fractional integrals Bull. Math. Anal. Appl., 2(3), pp. 93-99.
  • [3] Dragomir, S. S., (2002), Some integral inequalities of Gr¨uss type, Indian J. Pure Appl. Math., 31, pp. 397415.
  • [4] G¨ozpnar, A., C¸ elik, B. and Set, E., (2016), Hermite-Hadamard type inequalities for quasi-convex functions via conformable fractional integrals, Xth International Statistics Days Conference, Abstracts and Proceedings Book, pp. 537-543.
  • [5] Gr¨uss, D., (1935), Uber das maximum des absoluten Betrages von 1 b−a R b a f(x)g(x)dx − 1 (b−a) 2 R b a f(x)dx R b a g(x)dx, Math.Z., 39, pp. 215-226.
  • [6] Khalil, R., Al Horani, M., Yousef, A. and Sababheh, M., (2014), A new definition of fractional derivative, J. Comput. Appl. Math., 264 , pp. 65-70.
  • [7] Sarikaya , M. Z., (2008), A note on Gr¨uss type inequalities on time scales, Dynamic Systems and Appl., 17, pp. 663-666.
  • [8] Set, E. and Sarikaya, M. Z., (2011), On the generalization of Ostrowski and Gr¨uss type discrete inequalities, Comput. Math. Appl., 62 , pp. 455461.
  • [9] Set, E., G¨ozpinar, A. and Choi, J., (2017), Hermite-Hadamard Type Inequalities For Twice differentiable m-Convex Functions Via Conformable Fractional Integrals, Far East J. Math. Sci., 101(4), pp. 873-891.
  • [10] Set, E., Sarıkaya, M. Z. and G¨ozpınar, A., (2017), Some Hermite-Hadamard type inequalities for convex functions via conformable fractional integrals and related inequalities, Creative Math. Inform., 26(2).
  • [11] Set, E., G¨ozpınar, A. and Ekinci, A., Hermite-Hadamard type inequalities via conformable fractional integral, Acta Math. Univ. Comenianae, in press.
  • [12] Set, E., C¸ elik, B. and Korkut, N., (2016), On New Conformable Fractional Hermite-Hadamard Type Inequalities, Xth International Statistics Days Conference, Abstracts and Proceedings Book, pp. 793- 798.
  • [13] Set, E., Akdemir, A.O. and C¸ elik, B., (2016), Some Hermite-Hadamard Type Inequalities for Products of Two Different Convex Functions via Conformable Fractional Integrals, Xth International Statistics Days Conference, Abstracts and Proceedings Book, pp. 576-581.
  • [14] Set, E. and C¸ elik, B., (2017) Certain Hermite-Hadamard type inequalities associated with conformable fractional integral operators, Creative Math. Inform., 26(3).

ON NEW GRÜSS TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS

Year 2019, Volume 9, Issue 4, 01.12.2019

Abstract

We use conformable fractional integral, recently introduced by Khalil et. al. and Abdeljavad, to obtain some new integral inequalities of Gruss type. We show two new theorems associated with Gruss inequality, as well as state and show new identities related to this fractional integral operator.

References

  • [1] Abdeljawad, T., (2015), On conformable fractional calculus, J. Comput. Appl. Math., 279, pp. 57-66.
  • [2] Dahmani, Z., Tabharit, L. and Taf, S., (2010), New Generalization of Gr¨uss inequality using RiemannLiouville fractional integrals Bull. Math. Anal. Appl., 2(3), pp. 93-99.
  • [3] Dragomir, S. S., (2002), Some integral inequalities of Gr¨uss type, Indian J. Pure Appl. Math., 31, pp. 397415.
  • [4] G¨ozpnar, A., C¸ elik, B. and Set, E., (2016), Hermite-Hadamard type inequalities for quasi-convex functions via conformable fractional integrals, Xth International Statistics Days Conference, Abstracts and Proceedings Book, pp. 537-543.
  • [5] Gr¨uss, D., (1935), Uber das maximum des absoluten Betrages von 1 b−a R b a f(x)g(x)dx − 1 (b−a) 2 R b a f(x)dx R b a g(x)dx, Math.Z., 39, pp. 215-226.
  • [6] Khalil, R., Al Horani, M., Yousef, A. and Sababheh, M., (2014), A new definition of fractional derivative, J. Comput. Appl. Math., 264 , pp. 65-70.
  • [7] Sarikaya , M. Z., (2008), A note on Gr¨uss type inequalities on time scales, Dynamic Systems and Appl., 17, pp. 663-666.
  • [8] Set, E. and Sarikaya, M. Z., (2011), On the generalization of Ostrowski and Gr¨uss type discrete inequalities, Comput. Math. Appl., 62 , pp. 455461.
  • [9] Set, E., G¨ozpinar, A. and Choi, J., (2017), Hermite-Hadamard Type Inequalities For Twice differentiable m-Convex Functions Via Conformable Fractional Integrals, Far East J. Math. Sci., 101(4), pp. 873-891.
  • [10] Set, E., Sarıkaya, M. Z. and G¨ozpınar, A., (2017), Some Hermite-Hadamard type inequalities for convex functions via conformable fractional integrals and related inequalities, Creative Math. Inform., 26(2).
  • [11] Set, E., G¨ozpınar, A. and Ekinci, A., Hermite-Hadamard type inequalities via conformable fractional integral, Acta Math. Univ. Comenianae, in press.
  • [12] Set, E., C¸ elik, B. and Korkut, N., (2016), On New Conformable Fractional Hermite-Hadamard Type Inequalities, Xth International Statistics Days Conference, Abstracts and Proceedings Book, pp. 793- 798.
  • [13] Set, E., Akdemir, A.O. and C¸ elik, B., (2016), Some Hermite-Hadamard Type Inequalities for Products of Two Different Convex Functions via Conformable Fractional Integrals, Xth International Statistics Days Conference, Abstracts and Proceedings Book, pp. 576-581.
  • [14] Set, E. and C¸ elik, B., (2017) Certain Hermite-Hadamard type inequalities associated with conformable fractional integral operators, Creative Math. Inform., 26(3).

Details

Primary Language English
Journal Section Research Article
Authors

İ. MUMCU This is me
Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey.


E. SET This is me
Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, Turkey.

Publication Date December 1, 2019
Published in Issue Year 2019, Volume 9, Issue 4

Cite

Bibtex @ { twmsjaem760947, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2019}, volume = {9}, number = {4}, pages = { - 1}, title = {ON NEW GRÜSS TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS}, key = {cite}, author = {Mumcu, İ. and Set, E.} }