Research Article
BibTex RIS Cite

ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS

Year 2016, Volume: 4 Issue: 2, 79 - 86, 01.10.2016
https://izlik.org/JA65RK28AE

Abstract

In this paper we prove Hadamard-type inequalities for $k$-fractional Riemann-Liouville integrals and Hadamard-type inequalities for fractional Riemann-Liouville integrals are deduced. Also we deduced some well known results related to Hadamard inequality.

References

  • [1] R. Diaz, E. Pariguan, On hypergeometric functions and pochhammer k-symbol, Divulg. Mat. Vol:15, No.2 (2007), 179{192.
  • [2] M. Dalir, M. Bashour, Applications of fractional calculus, Appl. Math. Sci. Vol:4, No.21 (2010), 1021{1032.
  • [3] R. Goren o, F. Mainardi, Fractional Calculus: integral and di erential equations of fractional order, Springer Verlag, Wien, 1997, 223-276.
  • [4] A. Loverro, Fractional Calculus: History, De nitions and Applications for the Engineer, Department of Aerospace and Mechanical Engineering, University of Notre Dame, 2004.
  • [5] S. Mubeen, G. M. Habibullah, k-Fractional integrals and applications, Int. J. Contemp. Math. Sci. Vol:7 (2012), 89{94.
  • [6] S. Miller, B. Ross, An introduction to fractional calculus and fractional differential equations, John Wiley And Sons, Usa, 1993.
  • [7] I. Podlubni, Fractional di erential equations, Academic Press, San Diego, 1999.
  • [8] M. Z. Sarikaya, H. Yildirim, On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals, RGMIA Research Report Collection, 17 (2014), Article 98, 10 pp.

Year 2016, Volume: 4 Issue: 2, 79 - 86, 01.10.2016
https://izlik.org/JA65RK28AE

Abstract

References

  • [1] R. Diaz, E. Pariguan, On hypergeometric functions and pochhammer k-symbol, Divulg. Mat. Vol:15, No.2 (2007), 179{192.
  • [2] M. Dalir, M. Bashour, Applications of fractional calculus, Appl. Math. Sci. Vol:4, No.21 (2010), 1021{1032.
  • [3] R. Goren o, F. Mainardi, Fractional Calculus: integral and di erential equations of fractional order, Springer Verlag, Wien, 1997, 223-276.
  • [4] A. Loverro, Fractional Calculus: History, De nitions and Applications for the Engineer, Department of Aerospace and Mechanical Engineering, University of Notre Dame, 2004.
  • [5] S. Mubeen, G. M. Habibullah, k-Fractional integrals and applications, Int. J. Contemp. Math. Sci. Vol:7 (2012), 89{94.
  • [6] S. Miller, B. Ross, An introduction to fractional calculus and fractional differential equations, John Wiley And Sons, Usa, 1993.
  • [7] I. Podlubni, Fractional di erential equations, Academic Press, San Diego, 1999.
  • [8] M. Z. Sarikaya, H. Yildirim, On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals, RGMIA Research Report Collection, 17 (2014), Article 98, 10 pp.
There are 8 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

GHULAM Farıd This is me

ATIQ UR Rehman This is me

MOQUDDSA Zahra This is me

Submission Date April 3, 2015
Publication Date October 1, 2016
IZ https://izlik.org/JA65RK28AE
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Farıd, G., Rehman, A. U., & Zahra, M. (2016). ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics, 4(2), 79-86. https://izlik.org/JA65RK28AE
AMA 1.Farıd G, Rehman AU, Zahra M. ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS. Konuralp J. Math. 2016;4(2):79-86. https://izlik.org/JA65RK28AE
Chicago Farıd, GHULAM, ATIQ UR Rehman, and MOQUDDSA Zahra. 2016. “ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4 (2): 79-86. https://izlik.org/JA65RK28AE.
EndNote Farıd G, Rehman AU, Zahra M (October 1, 2016) ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics 4 2 79–86.
IEEE [1]G. Farıd, A. U. Rehman, and M. Zahra, “ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS”, Konuralp J. Math., vol. 4, no. 2, pp. 79–86, Oct. 2016, [Online]. Available: https://izlik.org/JA65RK28AE
ISNAD Farıd, GHULAM - Rehman, ATIQ UR - Zahra, MOQUDDSA. “ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4/2 (October 1, 2016): 79-86. https://izlik.org/JA65RK28AE.
JAMA 1.Farıd G, Rehman AU, Zahra M. ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS. Konuralp J. Math. 2016;4:79–86.
MLA Farıd, GHULAM, et al. “ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics, vol. 4, no. 2, Oct. 2016, pp. 79-86, https://izlik.org/JA65RK28AE.
Vancouver 1.GHULAM Farıd, ATIQ UR Rehman, MOQUDDSA Zahra. ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS. Konuralp J. Math. [Internet]. 2016 Oct. 1;4(2):79-86. Available from: https://izlik.org/JA65RK28AE
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.