Some fractional integral inequalities of Hermite Hadamard and Minkowski type


  • Jorge Eliecer Hernádez Hernández Universidad Centroccidental Lisandro Alvarado, Decanato de Ciencias Económicas y Empresariales, Av.20 esquina Av. Moran, Barquisimeto, Venezuela



Integral inequalities, Fractional integral operator


This article presents some fractional integral inequalities of the Hermite-Hadamard and Minkowski type using the fractional integral operator defined by R.K. Raina (2016) in [1], which generalize some previous results found by L. Bougoffa [5] and S.S. Dragomir [7].


Agarwal, R. P., Luo, M-J. & Raina, R. K. On Ostrowski Type Inequalities, Fasculli Mathematici. 2016; 56 : 5 - 27.

Beckenbach, E. & Bellman, R. An Introduction to inequalities, L.W. Silver Company, 1961.

Beckenbach, E. & Bellman, R. Inequalities, Springer-Verlag, Berlin, 1961.

Belarbi, S. & Dahmani, Z. On some new fractional integral inequalities. Journal on Inequalities in Pure and Applied Mathematics; 2009, 10(3): 1 - 5. pp.

Bougoffa, L. On Minkowski and Hardy Integral Inequalities. Jounal of Inequalities in Pure and Applied Mathematics. 2006; 7(2).

Dahmani, Z. On Minkowski and Hermite-Hadamard Integral Inequalities Via Fractional Integration. Annals of Functional Analysis; 2010, 1(1): 51 - 58.

Dragomir, S. S., Set, E. & Ozdemir, M. E. On the Hermite-Hadamard Inequality and Other Integral Inequalities Involving Two Functions. Journal of Inequalities and Applications; 2010, Article ID 148102: 1 - 9.

Gorenflo, R. & Mainardi, F. Fractional Calculus: Integral and Differential Equations of Fractional Order. CISM Courses and Lect., Springer, 378: 223 - 276.

Hadamard, J. Etude sur les proprietes des fonctions entieres et en particulier dúne fonction considree par Riemann. Journal de Mathématiques pur et appliqué; 1893, 58(1): 171- 215.

Hardy, G. H., Littlewood, J. E. & Pólya, G. Inequalities, Cambridge Press., London , 1934.

Hermite, Ch. Sur deux limites dúne integrale definie. Mathesis; 1883, 3(1): 1 -82.

Iqbal, M., Iqbal, B. M. & Nazeer, K. Generalization of Inequalities Analogous to Hermite-Hadamard Inequality via Fractional Integrals. Bulletin of the Korean Mathematical Society, 2015, 523:707 - 716.

Marinkovic, S., Rajkovic, P. & Stankovic, M. The inequalities for some types q-integrals. Computers and Mathematics with Applications; 2008, 56: 2490 - 2498.

Marshall, A. W. & Olkin, I. Inequalities: Theory of Majoration and Applications, Academic Press, 1979.

Miller, S. & Ross, B. An introduction to the Fractional Calculus and Fractional Differential Equations. 1993, John Wiley and Sons, USA.

Niculescu, C. P. & Persson, L. E. Convex functions and their applications, A comtemporary approach. CMS Books in Mathematics, 23, Springer Verlag, New York, 2006.

Raina, R.K. On Generalized Wright’s Hypergeometric Functions and Fractional Calculus Operators. East Asian Mathematical Journal; 2005, 21(2): 191 - 203. 191–203.

Sarikaya, M. Z., Set, E., Yaldiz, H. & Basak, N. Hermite- Hadamard’s inequalities for fractional integrals and related fractional inequalities. Mathematical and Computer Modelling, 2017, 57:2403 - 2407.

Tunc¸, T., Budak, H., Usta, F. & Sarikaya, M. Z. On new generalized fractional integral operators and related inequalities. Submitted article, ResearchGate. [12 November 2018.



How to Cite

Hernádez Hernández, J. E. (2019). Some fractional integral inequalities of Hermite Hadamard and Minkowski type. Selecciones Matemáticas, 6(01), 41-48.