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

Year 2016, Volume: 4 Issue: 2, 79 - 86, 01.10.2016

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

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 Articles
Authors

GHULAM Farıd This is me

ATIQ UR Rehman This is me

MOQUDDSA Zahra This is me

Publication Date October 1, 2016
Submission Date April 3, 2015
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.
AMA Farıd G, Rehman AU, Zahra M. ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS. Konuralp J. Math. October 2016;4(2):79-86.
Chicago Farıd, GHULAM, ATIQ UR Rehman, and MOQUDDSA Zahra. “ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4, no. 2 (October 2016): 79-86.
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 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, 2016.
ISNAD Farıd, GHULAM et al. “ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4/2 (October 2016), 79-86.
JAMA 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, 2016, pp. 79-86.
Vancouver Farıd G, Rehman AU, Zahra M. ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS. Konuralp J. Math. 2016;4(2):79-86.
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