Inequalities for α-fractional differentiable functions

In this article, we present an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals. As applications, we establish some inequalities for certain special means of two positive real numbers and give the error estimations for the trapezoidal formula.

[1]  Roshdi Khalil,et al.  CONFORMABLE FRACTIONAL HEAT DIFFERENTIAL EQUATION , 2014 .

[2]  Sever S Dragomir,et al.  THE HADAMARD INEQUALITIES FOR s-CONVEX FUNCTIONS IN THE SECOND SENSE , 1999 .

[3]  J. Hadamard,et al.  Etude sur les propriétés des fonctions entières et en particulier d'une fonction considérée par Riemann , 1893 .

[4]  E. Nwaeze,et al.  Some New Results on the New Conformable Fractional Calculus with Application Using D’Alambert Approach , 2016 .

[5]  Ravi P. Agarwal,et al.  Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula , 1998 .

[6]  S. Dragomir.  Two Mappings in Connection to Hadamard's Inequalities , 1992 .

[7]  D. Anderson.  Taylor’s Formula and Integral Inequalities for Conformable Fractional Derivatives , 2014, 1409.5888.

[8]  M. A. Hammad,et al.  ABEL'S FORMULA AND WRONSKIAN FOR CONFORMABLE FRACTIONAL DIFFERENTIAL EQUATIONS , 2014 .

[9]  M. Khan,et al.  Inequalities for Three Times Differentiable Functions , 2016 .

[10]  M. Adil Khan,et al.  Hermite-Hadamard Inequality for Fractional Integrals Via Eta-Convex functions , 2017 .

[11]  H. Yildirim,et al.  ON SOME HADAMARD-TYPE INEQUALITIES FOR h-CONVEX FUNCTIONS , 2008 .

[12]  Y. Chu,et al.  On the Fractional Difference Equations of Order (2,q) , 2011 .

[13]  S. Dragomir,et al.  REFINEMENTS OF THE HERMITE-HADAMARD INEQUALITY FOR CONVEX FUNCTIONS , 2005 .

[14]  M. Sababheh,et al.  A new definition of fractional derivative , 2014, J. Comput. Appl. Math..

[15]  M. Noor.  On Hadamard integral inequalities involving two log-preinvex functions. , 2007 .

[16]  P. K. Jain.  CONVEX FUNCTIONS AND THEIR APPLICATIONS , 1968 .

[17]  Yu-Ming Chu,et al.  Inequalities and infinite product formula for Ramanujan generalized modular equation function , 2018 .

[18]  M. Noor,et al.  Hermite-Hadamard inequalities for relative semi-convex functions and applications , 2014 .

[19]  Y. Chu,et al.  Refinements of transformation inequalities for zero-balanced hypergeometric functions , 2017 .

[20]  Yu-Ming Chu,et al.  Solution to the Linear Fractional Differential Equation Using Adomian Decomposition Method , 2011 .

[21]  Thabet Abdeljawad,et al.  On conformable fractional calculus , 2015, J. Comput. Appl. Math..

[22]  Josip Pečarić,et al.  Some inequalities of Hadamard type , 1995 .

[23]  Yu-Ming Chu,et al.  The Hermite-Hadamard Type Inequality of GA-Convex Functions and Its Application , 2010 .

[24]  Maslina Darus,et al.  Hadamard-Type Inequalities for s-Convex Functions , 2008 .

[25]  Sanja Varosanec,et al.  Properties of h-convex functions related to the Hermite-Hadamard-Fejér inequalities , 2009, Comput. Math. Appl..

[26]  Y. Chu,et al.  Generalizations of Hermite--Hadamard type inequalities for MT-convex functions , 2016 .

[27]  Y. Chu,et al.  Fractional Difference Equations with Real Variable , 2012 .

[28]  Constantin P. Niculescu,et al.  Convex Functions and Their Applications: A Contemporary Approach , 2005 .

[29]  W. Sulaiman.  Schur Convexity and Hadamard\'s Inequality , 2011 .

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

[31]  Feng Qi (祁锋),et al.  Hermite-Hadamard type inequalities for the m- and (α, m)-logarithmically convex functions , 2013 .