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.
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
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.
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.