Applying GG-Convex Function to Hermite-Hadamard Inequalities Involving Hadamard Fractional Integrals

By virtue of fractional integral identities, incomplete beta function, useful series, and inequalities, we apply the concept of GG-convex function to derive new type Hermite-Hadamard inequalities involving Hadamard fractional integrals. Finally, some applications to special means of real numbers are demonstrated.

[1]  V. Lakshmikantham,et al.  Theory of Fractional Dynamic Systems , 2009 .

[2]  Jinrong Wang,et al.  Fractional Integral Inequalities for Differentiable Convex Mappings and Applications to Special Means and a Midpoint Formula , 2012 .

[3]  Michal Feckan,et al.  Hermite–Hadamard-type inequalities for r-convex functions based on the use of Riemann–Liouville fractional integrals , 2013, Ukrainian Mathematical Journal.

[4]  Mehmet Zeki Sarikaya,et al.  Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities , 2013, Math. Comput. Model..

[5]  V. E. Tarasov.  Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media , 2011 .

[6]  Hari M. Srivastava,et al.  Some further refinements and extensions of the Hermite-Hadamard and Jensen inequalities in several variables , 2011, Math. Comput. Model..

[7]  Marek W. Michalski.  Derivatives of noninteger order and their applications , 1993 .

[8]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[9]  Riemann-Liouville Fractional Hermite-Hadamard Inequalities for differentiable λφ-preinvex functions , 2016 .

[10]  Riemann-Liouville fractional Hermite-Hadamard inequalities. Part I: for once differentiable geometric-arithmetically s-convex functions , 2013 .

[11]  W. Marsden.  I and J , 2012 .

[12]  Erhan Set,et al.  New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals , 2011, Comput. Math. Appl..

[13]  JinRong Wang,et al.  On some new Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals , 2013 .

[14]  C. E. M. Pearce,et al.  Inequalities for differentiable mappings with application to special means and quadrature formulæ , 2000, Appl. Math. Lett..

[15]  Jinrong Wang,et al.  Exploring s-e-condition and applications to some Ostrowski type inequalities via Hadamard fractional integrals , 2014 .

[16]  Yong Zhou,et al.  Hermite–Hadamard-type inequalities for Riemann–Liouville fractional integrals via two kinds of convexity , 2013 .

[17]  A. Luo,et al.  Fractional Dynamics and Control , 2011 .

[18]  Constantin P. Niculescu.  CONVEXITY ACCORDING TO MEANS , 2003 .

[19]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies) , 2006 .

[20]  Jinrong Wang,et al.  Refinements of Hermite-Hadamard Type Inequalities Involving Fractional Integrals , 2013 .

[21]  K. Diethelm.  The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type , 2010 .

[22]  New generalized Hermite-Hadamard type inequalities and applications to special means , 2013 .

[23]  I. Podlubny.  Fractional differential equations , 1998 .

[24]  Jinrong Wang,et al.  Fractional Hermite-Hadamard inequalities for (α,m)-logarithmically convex functions , 2013, Journal of Inequalities and Applications.