jum Journal of Universal Mathematics 2618-5660 2618-5660 Gökhan ÇUVALCIOĞLU 10.33773/jum.506507 Mathematical Sciences Matematik GENERALIZATION MITTAG-LEFFLER FUNCTION ASSOCIATED WITH OF THE HADAMARD AND FEJER HADAMARD INEQUALITIES FOR (h-m)-STRONGLY CONVEX FUNCTIONS VIA FRACTIONAL INTEGRALS Kılınç Seda Kahramanmaras Sütcü Imam University Akkurt Abdullah Kahramanmaras Sütcü Imam University Yıldırım Hüseyin Kahramanmaras Sütcü Imam University 01 30 2019 2 1 8 15 01 02 2019 01 26 2019 Copyright © 2018, Journal of Universal Mathematics 2018 Journal of Universal Mathematics

The aim of this paper, Hadamard and Fejer Hadamard _nequalities for (h -m)-strongly convex functions viageneralizeed fractional integral operators involving the generalizedMittag-Le_er function are established. In particular several knows results arementioned.

 Hermite-Hadamard inequality -convex fuction Ozdemir M, Akdemri A, Set E. On (h - m)-convexity and hadamard-type inequalities. Transylvanian Journal of Mathematics and Mechanics. 2016;8(1):51- 58.Varosanec S. On h-convexity. Journal of Mathematical Analysis and Applications.2007;326(1):303-311.Kilbas A, Srivastava H, Trujillo J. Theory and applications of fractional di_erential equations. Elsevier, Amsterdam; 2006.C. R. Bector and C. Singh, B-Vex functions, J. Optim. Theory. Appl. 71 (2) (1991) 237-253Podlubni I. Fractional di_erential equations. Academic press. San Diego; 1999. Farid G. Weighted opial inequalities for fractional integral and di_erential operators involving generalized Mittag-Le_er function. European Journal of Pure and Applied Mathematics. 2017;10(3):419-439.Srivastava H, Tomovski Z. Fractional calculus with an integral operator containing generalized Mittagle_er function in the kernel. Applied Mathematics and Computation. 2009;211(1):198-210.Prabhakar T. A singular integral equation with a generalized Mittag-le_er function in the kernel. Yokohama Mathematical Journal. 1971;19:7-15. Chen F. On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals via two kinds of convexity. Chinese Journal of Mathematics. 2014; Article ID 173293.Chen H, Katugampola U. Hermite-Hadamard-Fejr type inequalities for generalized fractional integrals. Journal of Mathematical Analysis and Applications. 2017;446:1274-1291.Farid G. A Treatment of the Hadamard inequality due to m- convexity via generalized fractional integral. Fractional Calculus and Applied Analysis. In press.Farid G, Rehman AU, Tariq B. On Hadamard-type inequalities for m-convex functions via Riemann-Liouville fractional integrals. Studia Universitatis Babes_-Bolyai Mathematica. 2017;62(2):141-150.Loverro A. Fractional calculus: history, de_nitions and applications for the engineers. Rapport technique. University of Notre Dame: Department of Aerospace and Mechanical Engineering. 2004:1-28.Arqub O, El-Ajou A, Momani S. Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial di_erential equations. Journal of Computational Physics. 2015;293:385-399.El-Ajou A, Arqub O, Momani S. Approximate analytical solution of the nonlinear fractional KdV-burgers equation : a new iterative algorithm. Journal of Computational Physics. 2015;293 :81-95.El-Ajou A, Arqub O, Momani S, Baleanu D, Alsaedi A. A novel expansion iterative method for solving linear partial di_erential equations of fractional order. Applied Mathematics and Computation. 2015;257:119-133.Arqub O. Fitted reproducing kernel hilbert space method for the solutions of some certain classes of time-fractional partial di_erential equations subject to initial and neumann boundary conditions. Computers & Mathematics with Applications. 2017;73:1243-1261.M. E.ozdemir, M. Avci and H. Kavurmaci, Hermite-Hadamard-type inequalities via ( _;m)- convexity. Comput. Math. Appl. 61 (2011), no. 9, 2614-2620Farid G. Hadamard and Fej _er-Hadamard inequalities for generalized fractional integral involving special functions. Konuralp Journal of Mathematics. 2016;4(1):108-113.Sarikaya M, Set E, Yaldiz H, Basak N. Hermite-Hadamards inequalities for fractional integrals and related fractional inequalities. Mathematical and Computer Modelling. 2013;57:2403- 2407.Sarikaya M, Yildirim H. On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals. Miskolc Mathematical Notes. 2016;17(2):1049-1059.A. U. Rehman, G.Farid and Q.U. Ain Hadamard and Fej_er Hadamard Inequalities for (h -m)- Convex Functions Via Fractional Integral Containing the Generalized Mittag-Le_er Function Journal of Scienti_c Research reports 2018; 18(5); 1-8.