Some New Fractional Inequalities Involving Convex Functions and Generalized Fractional Integral Operator

Author:

Neamah Majid K.12ORCID,Ibrahim Alawiah2ORCID,Mehdy Hala Shaker3ORCID,Redhwan Saleh S.4ORCID,Abdo Mohammed S.5ORCID

Affiliation:

1. Department of Mathematics, College of Sciences, University of Baghdad, Baghdad, Iraq

2. Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

3. College of Education, Computer Science, Al-Mustansiriya University, Baghdad, Iraq

4. Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, M.S, 431001, Aurangabad, India

5. Department of Mathematics, Hodeidah University, Al-Hudaydah, Yemen

Abstract

In this manuscript, we are getting some novel inequalities for convex functions by a new generalized fractional integral operator setting. Our results are established by merging the k , s -Riemann-Liouville fractional integral operator with the generalized Katugampola fractional integral operator. Certain special instances of our main results are considered. The detailed results extend and generalize some of the present results by applying some special values to the parameters.

Publisher

Hindawi Limited

Subject

Analysis

Reference33 articles.

1. Sur les expressions approximatives des integrales definies par les autres prises entre les memes limites;P. L. Chebyshev;Proceedings of Mathematical Society of Charkov,1882

2. On some new fractional integral inequalities;S. Belarbi;Journal of Inequalities in Pure and Applied Mathematics,2009

3. Certain inequalities related to the Chebyshev functional involving a Riemann-Liouville operator;Z. Dahmani;Bulletin of Mathematical Analysis and Applications,2011

4. Some integral inequalities of Gr uss type;S. S. Dragomir;Indian Journal of Pure and Applied Mathematics,2000

5. Certain Grüss type inequalities involving the generalized fractional integral operator

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