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