%0 Journal Article %T Error bounds associated with different versions of Hadamard inequalities of mid-point type %A Raees, Muhammad %A Anwar, Matloob %A Farid, Ghulam %J Journal of Mathematics and Computer Science %D 2021 %V 23 %N 3 %@ ISSN 2008-949X %F Raees2021 %X In this paper, we establish the error bounds of different versions of mid-point type inequalities. At first, we prove two identities for fractional integrals involving the extended generalized Mittag-Leffler function and generalized exponential fractional integrals, and then we establish the corresponding error bound inequalities. Furthermore, we find a generalized inequality for error bound inequalities using a generalized identity. Also, we find some inequalities which formulate all error bound inequalities for various versions of Hadamard inequality. Finally, we present some examples of the central moment of a random variable. %9 journal article %R 10.22436/jmcs.023.03.05 %U http://dx.doi.org/10.22436/jmcs.023.03.05 %P 213--229 %0 Journal Article %T Some inequalities for the dispersion of a random variable whose pdf is defined on a finite interval %A N. S. Barnett %A P. Cerone %A S. S. Dragomir %A J. Roumeliotis %J J. Inequal. Pure Appl. Math. %D 2001 %V 2 %F Barnett2001 %0 Journal Article %T Some elementary inequalities for the expectation and variance of a random variable whose pdf is defined on a finite interval %A N. S. Barnett %A S. S. Dragomir %J Nova Sci. Publ. %D 2002 %V 2 %F Barnett2002 %0 Journal Article %T New generalization of Hermite-Hadamard type inequalities via generalized fractional integrals %A H. Budak %A F. Ertugral %A M. Z. Sarikaya %J %D %V %F Budak %0 Journal Article %T On some inequalities for the expectation and variance %A P. Cerone %A S. S. Dragomir %J Korean J. Comput. Appl. Math. %D 2001 %V 8 %F Cerone2001 %0 Journal Article %T Inequalities of Jensen's type for generalized $k$-$g$-Fractional integrals of functions for which the composite $f\circ g^{-1}$ is convex %A S. S. Dragomir %J Fract. Differ. Calc. %D 2018 %V 8 %F Dragomir2018 %0 Journal Article %T Existence of an integral operator and its consequences in fractional calculus %A G. Farid %J Open J. Math. Sci. %D 2019 %V 3 %F Farid2019 %0 Journal Article %T Bounds associated to Hadamard inequality via generalized integral operators and applications for conformable and fractional integrals %A G. Farid %A M. Raees %A M. Anwar %J J. Fract. Calc. Appl. %D 2020 %V 11 %F Farid2020 %0 Journal Article %T Hermite-Hadamard inequalities in fractional calculus defined using Mittag-Leffler kernels %A A. Fernandez %A P. O. Mohammed %J Math. Methods Appl. Sci. %D 2020 %V 2020 %F Fernandez2020 %0 Journal Article %T Hadamard and Fejer–Hadamard inequalities for extended generalized fractional integrals involving special functions %A S. M. Kang %A G. Farid %A W. Nazeer %A B. Tariq %J J. Inequal. Appl. %D 2018 %V 2018 %F Kang2018 %0 Book %T Theory and applications of fractional differential equations %A A. A. Kilbas %A H. M. Srivastava %A J. J. Trujillo %D 2006 %I Elsevier Science B.V. %C Amsterdam %F Kilbas2006 %0 Journal Article %T Moments inequalities of a random variable defined over a finite interval %A P. Kumar %J JIPAM. J. Inequal. Pure Appl. Math. %D 2002 %V 3 %F Kumar2002 %0 Journal Article %T Inequalities involving moments of a continuous random variable defined over a finite interval %A P. Kumar %J Comput. Math. Appl. %D 2004 %V 48 %F Kumar2004 %0 Journal Article %T Generalized Riemann-Liouville $k$-fractional integrals associated with Ostrowski type inequalities and error bounds of Hadamard Inequalities %A Y. C. Kwun %A G. Farid %A W %A Nazeer %A S. Ullah %A S. M. Kang %J IEEE Access %D 2018 %V 6 %F Kwun2018 %0 Journal Article %T Hermite-Hadamard inequalities for Riemann-Liouville fractional integrals of a convex function with respect to a monotone function %A P. O. Mohammed %J Math. Meth. Appl. Sci. %D 2019 %V 2019 %F Mohammed2019 %0 Journal Article %T Modification of certain fractional integral inequalities for convex functions %A P. O. Mohammed %A T. Abdeljawad %J Adv. Difference Equ. %D 2020 %V 2020 %F Mohammed2020 %0 Journal Article %T A New Version of the Hermite-Hadamard Inequality for Riemann-Liouville Fractional Integrals %A P. O. Mohammed %A I. Brevik %J Symmetry %D 2020 %V 12 %F Mohammed2020 %0 Journal Article %T On generalized fractional integral inequalities for twice differentiable convex functions %A P. O. Mohammad %A M. Z. Sarikaya %J J. Comput. Appl. Math. %D 2020 %V 372 %F Mohammad2020 %0 Journal Article %T On the Generalized Hermite-Hadamard Inequalities via the Tempered Fractional Integrals %A P. O. Mohammed %A M. Z. Sarikaya %A D. Baleanu %J Symmetry %D 2020 %V 12 %F Mohammed2020 %0 Book %T Fractional Integrals and Derivatives %A S. G. Samko %A A. A. Kilbas %A O. I. Marichev %D 1993 %I Gordon and Breach Science Publishers %C Yverdon %F Samko1993 %0 Journal Article %T Hermite--Hadamard's inequlities for fractional integrals and related fractional inequalitis %A M. Z. Sarikaya %A E. Set %A H. Yaldiz %A N. Başak %J Math. Comput. Modelling %D 2013 %V 57 %F Sarikaya2013 %0 Journal Article %T Hermite-Hadamard type inequalities for the generalized $k$-fractional integral operators %A E. Set %A J. S. Choi %A A. Gözpinar %J J. Inequal. Appl. %D 2017 %V 2017 %F Set2017 %0 Journal Article %T On new generalized fractional integral operators and related fractional inequalities %A T. Tunc %A H. Budak %A F. Usta %A M.Z. Sarikaya %J %D %V %F Tunc