On Gru ̈ ss Type Inequality Involving a Fractional Integral Operator with a Multi-Index Mittag-Leffler Function as a Kernel

Authors

Kamlesh Jangid, Department of HEAS(Mathematics), Rajasthan Technical University, Kota, Rajasthan, IndiaFollow
Sunil Dutt Purohit, Department of HEAS(Mathematics), Rajasthan Technical University, Kota, Rajasthan, IndiaFollow
Ritu Agarwal, Department of Mathematics, Malaviya National Institute of Technology, Jaipur, IndiaFollow

Author Country (or Countries)

India

Abstract

Manydisciplinesofpureandappliedmathematicshavefoundfractionalintegralinequalitiestobeoneofthemostsignificant and powerful instruments for their progress. These inequalities get a variety of applications in numerical quadrature, transform theory, probability, and statistical problems, however the most relevant one is determining the uniqueness of fractional boundary value problem solutions. They also offer upper and lower limits for the solutions to the equations above. Among this article, we define an integral inequality of Gru ̈ss type linked to the bounded integrable function associated with the fractional integral operator, which involves the generalized multi-index Mittag-Leffler function as a kernel. Our key finding is of a general nature and may give rise, as a special case, to integral inequalities of the type Gru ̈ss representing different fractional integral operators described in the literature.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/160214

Recommended Citation

Jangid, Kamlesh; Dutt Purohit, Sunil; and Agarwal, Ritu (2022) "On Gru ̈ ss Type Inequality Involving a Fractional Integral Operator with a Multi-Index Mittag-Leffler Function as a Kernel," Applied Mathematics & Information Sciences: Vol. 16: Iss. 2, Article 14.
DOI: http://dx.doi.org/10.18576/amis/160214
Available at: https://digitalcommons.aaru.edu.jo/amis/vol16/iss2/14