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Katugampola Fractional Integrals within the Class of Convex Functions

Year 2018, Volume: 3 Issue: 1, 40 - 50, 31.12.2018

Abstract

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.

References

  • 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.
Year 2018, Volume: 3 Issue: 1, 40 - 50, 31.12.2018

Abstract

References

  • 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.
There are 15 citations in total.

Details

Primary Language English
Journal Section Volume III, Issue I, 2018
Authors

Hatice Yaldız

Ahmet Ocak Akdemir

Publication Date December 31, 2018
Published in Issue Year 2018 Volume: 3 Issue: 1

Cite

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. December 2018;3(1):40-50.
Chicago Yaldız, Hatice, and Ahmet Ocak Akdemir. “Katugampola Fractional Integrals Within the Class of Convex Functions”. Turkish Journal of Science 3, no. 1 (December 2018): 40-50.
EndNote Yaldız H, Akdemir AO (December 1, 2018) Katugampola Fractional Integrals within the Class of Convex Functions. Turkish Journal of Science 3 1 40–50.
IEEE H. Yaldız and A. O. Akdemir, “Katugampola Fractional Integrals within the Class of Convex Functions”, TJOS, vol. 3, no. 1, pp. 40–50, 2018.
ISNAD Yaldız, Hatice - Akdemir, Ahmet Ocak. “Katugampola Fractional Integrals Within the Class of Convex Functions”. Turkish Journal of Science 3/1 (December 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 and Ahmet Ocak Akdemir. “Katugampola Fractional Integrals Within the Class of Convex Functions”. Turkish Journal of Science, vol. 3, no. 1, 2018, pp. 40-50.
Vancouver Yaldız H, Akdemir AO. Katugampola Fractional Integrals within the Class of Convex Functions. TJOS. 2018;3(1):40-5.