Some New Fractional Integral Inequalities Pertaining to Generalized Fractional Integral Operator

Abstract

Integral inequalities make up a comprehensive and prolific field of research within the field of mathematical interpretations. Integral inequalities in association with convexity have a strong relationship with symmetry. Different disciplines of mathematics and applied sciences have taken a new path as a result of the development of new fractional operators. Different new fractional operators have been used to improve some mathematical inequalities and to bring new ideas in recent years. To take steps forward, we prove various Grüss-type and Chebyshev-type inequalities for integrable functions in the frame of non-conformable fractional integral operators. The key results are proven using definitions of the fractional integrals, well-known classical inequalities, and classical relations.

On a General Formulation of the Riemann–Liouville Fractional Operator and Related Inequalities

“…On the other hand, if we take F ≡ 1 and k = 1, it is clear that Theorem 3.1 of [23] is a particular case of our result. Under the last assumption, we can easily formulate a more general result than Theorem 4 of [24] and all the results of [25].…”

Norm and Numerical Radius Inequalities for Sums of Power Series of Operators in Hilbert Spaces

“…These concepts are used in different parts of mathematics. Previous research, including the studies referenced in [1][2][3][4][5][6][7][8][9][10], has extensively investigated mathematical inequalities and discovered significant findings. These studies provide a foundation for future research in this field.…”