ON NEW GRÜSS TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS

Volume: 9 Number: 4 December 1, 2019
  • İ. Mumcu
  • E. Set
EN

ON NEW GRÜSS TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS

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.

Keywords

References

  1. [1] Abdeljawad, T., (2015), On conformable fractional calculus, J. Comput. Appl. Math., 279, pp. 57-66.
  2. [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. [3] Dragomir, S. S., (2002), Some integral inequalities of Gr¨uss type, Indian J. Pure Appl. Math., 31, pp. 397415.
  4. [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. [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. [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. [7] Sarikaya , M. Z., (2008), A note on Gr¨uss type inequalities on time scales, Dynamic Systems and Appl., 17, pp. 663-666.
  8. [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.

Details

Primary Language

English

Subjects

-

Journal Section

-

Authors

İ. Mumcu This is me

Publication Date

December 1, 2019

Submission Date

-

Acceptance Date

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Published in Issue

Year 2019 Volume: 9 Number: 4

APA
Mumcu, İ., & Set, E. (2019). ON NEW GRÜSS TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS. TWMS Journal of Applied and Engineering Mathematics, 9(4), 1. https://izlik.org/JA35WH97ZS
AMA
1.Mumcu İ, Set E. ON NEW GRÜSS TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS. JAEM. 2019;9(4):1. https://izlik.org/JA35WH97ZS
Chicago
Mumcu, İ., and E. Set. 2019. “ON NEW GRÜSS TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS”. TWMS Journal of Applied and Engineering Mathematics 9 (4): 1. https://izlik.org/JA35WH97ZS.
EndNote
Mumcu İ, Set E (December 1, 2019) ON NEW GRÜSS TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS. TWMS Journal of Applied and Engineering Mathematics 9 4 1.
IEEE
[1]İ. Mumcu and E. Set, “ON NEW GRÜSS TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS”, JAEM, vol. 9, no. 4, p. 1, Dec. 2019, [Online]. Available: https://izlik.org/JA35WH97ZS
ISNAD
Mumcu, İ. - Set, E. “ON NEW GRÜSS TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS”. TWMS Journal of Applied and Engineering Mathematics 9/4 (December 1, 2019): 1. https://izlik.org/JA35WH97ZS.
JAMA
1.Mumcu İ, Set E. ON NEW GRÜSS TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS. JAEM. 2019;9:1.
MLA
Mumcu, İ., and E. Set. “ON NEW GRÜSS TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS”. TWMS Journal of Applied and Engineering Mathematics, vol. 9, no. 4, Dec. 2019, p. 1, https://izlik.org/JA35WH97ZS.
Vancouver
1.İ. Mumcu, E. Set. ON NEW GRÜSS TYPE INEQUALITIES FOR CONFORMABLE FRACTIONAL INTEGRALS. JAEM [Internet]. 2019 Dec. 1;9(4):1. Available from: https://izlik.org/JA35WH97ZS