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

Yıl 2016, Cilt: 4 Sayı: 2, 79 - 86, 01.10.2016

GHULAM Farıd ATIQ UR Rehman MOQUDDSA Zahra

Öz

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.

Anahtar Kelimeler

Convex functions Hadamard inequalities fractional integral

Kaynakça

  • [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.

Yıl 2016, Cilt: 4 Sayı: 2, 79 - 86, 01.10.2016

GHULAM Farıd ATIQ UR Rehman MOQUDDSA Zahra

Öz

Kaynakça

  • [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.
Toplam 8 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

GHULAM Farıd

ATIQ UR Rehman

MOQUDDSA Zahra

Yayımlanma Tarihi 1 Ekim 2016
Gönderilme Tarihi 3 Nisan 2015
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 2

Kaynak Göster

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. Ekim 2016;4(2):79-86.
Chicago Farıd, GHULAM, ATIQ UR Rehman, ve MOQUDDSA Zahra. “ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4, sy. 2 (Ekim 2016): 79-86.
EndNote Farıd G, Rehman AU, Zahra M (01 Ekim 2016) ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics 4 2 79–86.
IEEE G. Farıd, A. U. Rehman, ve M. Zahra, “ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS”, Konuralp J. Math., c. 4, sy. 2, ss. 79–86, 2016.
ISNAD Farıd, GHULAM vd. “ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics 4/2 (Ekim 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 vd. “ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS”. Konuralp Journal of Mathematics, c. 4, sy. 2, 2016, ss. 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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