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Katugampola Fractional Integrals within the Class of Convex Functions

Yıl 2018, Cilt: 3 Sayı: 1, 40 - 50, 31.12.2018

Öz

The aim of this
paper is to the Hermite-Hadamard type inequalities for functions whose first
derivatives in absolute value is s-convex through the instrument of generalized
Katugampola fractional integrals.

Kaynakça

  • W.W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math. 23(1978), 13-20.
  • F. Chen, A note on the Hermite-Hadamard inequality for convex functions on the coordinates, J. of Math. Inequalities, 8(4), (2014) 915-923.
  • H. Chen, U.N. Katugampola, Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for generalized fractional integrals, J.Math. Anal. Appl., 446 (2017), 1274-1291.
  • G. Cristescua, Boundaries of Katugampola fractional integrals within the class of convex functions, https://www.researchgate.net/publication/313161140.
  • A. Erdélyi, On fractional integration and its application to the theory of Hankel transforms, The Quarterly Journal of Mathematics, Oxford, Second Series, 11(1940), 293-303.
  • R. Gorenflo and F. Mainardi, Fractinal calculus: integral and differential equations of fractional order, Springer Verlag, Wien (1997), 223-276.
  • J. Hadamard, Etude sur les proprietes des fonctions entieres et en particulier d’une fonction considree par, Riemann, J. Math. Pures. et Appl. 58 (1893), 171-215.
  • H. Hudzik and L. Maligranda, Some remarks on convex functions, Acquationes Math. 48 (1994), 100-111.
  • U. N. Katugampola, New approach to a generalized fractional integrals, Appl. Math. Comput., 218 (4) (2011), 860-865.
  • U. N. Katugampola, New approach to a generalized fractional derivatives, Bull. Math. Anal. Appl., Volume 6 Issue 4 (2014), Pages 1-15.
  • A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, 204, Elsevier Sci. B.V., Amsterdam, 2006.
  • H. Kober, On fractional integrals and derivatives, The Quarterly J. Math. ( Oxford Series), 11 (1) (1940), 193-211.
  • S. Miller and B. Ross, An introduction to the fractional calculusand fractional differential equations, John Wiley & Sons, USA, 1993, p.2.
  • M. Z. Sarıkaya, E. Set, H. Yaldiz, N. Ba ak , Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math Comput Model. 2013;57(9-10):2403-2407.
  • M. Z. Sarıkaya and H. Yildirim, On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals, Miskolc Mathematical Notes, Vol. 17 (2016), No. 2, pp. 1049-1059.
Yıl 2018, Cilt: 3 Sayı: 1, 40 - 50, 31.12.2018

Öz

Kaynakça

  • W.W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter konvexer funktionen in topologischen linearen Raumen, Pupl. Inst. Math. 23(1978), 13-20.
  • F. Chen, A note on the Hermite-Hadamard inequality for convex functions on the coordinates, J. of Math. Inequalities, 8(4), (2014) 915-923.
  • H. Chen, U.N. Katugampola, Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for generalized fractional integrals, J.Math. Anal. Appl., 446 (2017), 1274-1291.
  • G. Cristescua, Boundaries of Katugampola fractional integrals within the class of convex functions, https://www.researchgate.net/publication/313161140.
  • A. Erdélyi, On fractional integration and its application to the theory of Hankel transforms, The Quarterly Journal of Mathematics, Oxford, Second Series, 11(1940), 293-303.
  • R. Gorenflo and F. Mainardi, Fractinal calculus: integral and differential equations of fractional order, Springer Verlag, Wien (1997), 223-276.
  • J. Hadamard, Etude sur les proprietes des fonctions entieres et en particulier d’une fonction considree par, Riemann, J. Math. Pures. et Appl. 58 (1893), 171-215.
  • H. Hudzik and L. Maligranda, Some remarks on convex functions, Acquationes Math. 48 (1994), 100-111.
  • U. N. Katugampola, New approach to a generalized fractional integrals, Appl. Math. Comput., 218 (4) (2011), 860-865.
  • U. N. Katugampola, New approach to a generalized fractional derivatives, Bull. Math. Anal. Appl., Volume 6 Issue 4 (2014), Pages 1-15.
  • A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, 204, Elsevier Sci. B.V., Amsterdam, 2006.
  • H. Kober, On fractional integrals and derivatives, The Quarterly J. Math. ( Oxford Series), 11 (1) (1940), 193-211.
  • S. Miller and B. Ross, An introduction to the fractional calculusand fractional differential equations, John Wiley & Sons, USA, 1993, p.2.
  • M. Z. Sarıkaya, E. Set, H. Yaldiz, N. Ba ak , Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math Comput Model. 2013;57(9-10):2403-2407.
  • M. Z. Sarıkaya and H. Yildirim, On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals, Miskolc Mathematical Notes, Vol. 17 (2016), No. 2, pp. 1049-1059.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Volume III, Issue I, 2018
Yazarlar

Hatice Yaldız

Ahmet Ocak Akdemir

Yayımlanma Tarihi 31 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 3 Sayı: 1

Kaynak Göster

APA Yaldız, H., & Akdemir, A. O. (2018). Katugampola Fractional Integrals within the Class of Convex Functions. Turkish Journal of Science, 3(1), 40-50.
AMA Yaldız H, Akdemir AO. Katugampola Fractional Integrals within the Class of Convex Functions. TJOS. Aralık 2018;3(1):40-50.
Chicago Yaldız, Hatice, ve Ahmet Ocak Akdemir. “Katugampola Fractional Integrals Within the Class of Convex Functions”. Turkish Journal of Science 3, sy. 1 (Aralık 2018): 40-50.
EndNote Yaldız H, Akdemir AO (01 Aralık 2018) Katugampola Fractional Integrals within the Class of Convex Functions. Turkish Journal of Science 3 1 40–50.
IEEE H. Yaldız ve A. O. Akdemir, “Katugampola Fractional Integrals within the Class of Convex Functions”, TJOS, c. 3, sy. 1, ss. 40–50, 2018.
ISNAD Yaldız, Hatice - Akdemir, Ahmet Ocak. “Katugampola Fractional Integrals Within the Class of Convex Functions”. Turkish Journal of Science 3/1 (Aralık 2018), 40-50.
JAMA Yaldız H, Akdemir AO. Katugampola Fractional Integrals within the Class of Convex Functions. TJOS. 2018;3:40–50.
MLA Yaldız, Hatice ve Ahmet Ocak Akdemir. “Katugampola Fractional Integrals Within the Class of Convex Functions”. Turkish Journal of Science, c. 3, sy. 1, 2018, ss. 40-50.
Vancouver Yaldız H, Akdemir AO. Katugampola Fractional Integrals within the Class of Convex Functions. TJOS. 2018;3(1):40-5.