TY - JOUR T1 - On generalization of different type inequalities for (α,m)-convex functions via fractional integrals AU - Iscan, İmdat AU - Aydin, Mustafa AU - Bekar, Kerim PY - 2016 DA - September JF - New Trends in Mathematical Sciences PB - Mustafa BAYRAM WT - DergiPark SN - 2147-5520 SP - 49 EP - 57 VL - 4 IS - 3 LA - en AB -  In this paper,new identity for fractional integrals have been defined. By using of thisidentity, the authors obtained new general inequalities containing all ofHadamard, Ostrowski and Simpson type inequalities for functions whosederivatives in absolute value at certain power are -convex via Riemann Liouville fractional integral. KW - Hermite–Hadamard inequality KW - Riemann–Liouville fractional integral KW - (α CR - M. Abramowitz and I.A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1965. CR - M.K. Bakula, M.E. Ozdemir and J. Pecaric, Hadamard type inequalities for m-convex and (α,m)-convex functions, J. Inequal. Pure Appl. Math. 9(4) (2008) Article 96, p. 12. [Online: http://jipam.vu.edu.au/article.php?sid=1032]. CR - R. Gorenflo and F. Mainardi,Fractional calculus, integral and differential equations of fractional order, Springer Verlag, Wien, 1997, 223-276. CR - I. Iscan, A new generalization of some integral inequalities for (α,m)-convex functions, Mathematical Sciences 7(22) (2013)1-8. CR - I. Iscan, New estimates on generalization of some integral inequalities for (α,m)-convex functions, Contemp. Anal. Appl. Math. 1(2) (2013), 253-264 . CR - I. Iscan, Hermite-Hadamard type inequalities for functions whose derivatives are (α,m)-convex, International Journal of Engineering and Applied sciences 2(3) (2013), 69-78. CR - V.G. Miheşan, A generalization of the convexity. Seminer on Functional Equations, Approximation and Convexity, Cluj-Napoca, Romania, 1993. CR - S. Miller and B. Ross, An introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, USA, 1993. CR - M.E. Ozdemir, M. Avcı and H. Kavurmacı, Hermite-Hadamard-type inequalities via (α,m)-convexity, Comput. Math. Appl. 61 (2011), 2614-2620. CR - M.E. Ozdemir, H. Kavurmacı and E. Set, Ostrowski’s type inequalities for (α,m)-convex functions, Kyungpook Math. J. 50 (2010), 371-378. CR - J. Park, Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable (α,m)-Convex Mappings, Int. J. Math. Math. Sci. 2012 (2012), Article ID 809689, 12 pages . doi:10.1155/2012/809689. CR - I. Podlubni, Fractional Differential Equations, Academic Press, San Diego, 1999. CR - M.Z. Sarıkaya and N. Aktan, On the generalization of some integral inequalities and their applications, Math. Comput. Modelling 54 (2011), 2175-2182 . CR - M.Z. Sarıkaya and H. Ogunmez, On new inequalities via Riemann-Liouville fractional integration, Abstr. Appl. Anal. 2012 (2012), Article ID 428983, 10 pages. doi:10.1155/2012/428983. Zbl 1253.26012. CR - M.Z. Sarıkaya, E. Set, H. Yaldız and N. Başak, Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math. Comput. Modelling 57(9-10) (2013), 2403-2407. CR - G. Toader, Some generalizations of the convexity, Proceedings of The Colloquium On Approximation And Optimization, Univ. Cluj-Napoca, Cluj-Napoca,1985, 329-338. UR - https://dergipark.org.tr/en/pub/ntims/issue//519496 L1 - https://dergipark.org.tr/en/download/article-file/637183 ER -