Certain Inequalities Pertaining to Some New Generalized Fractional Integral Operators

Date

2021

Authors

Srivastava, H.M.
Kashuri, Artion
Mohammed, Pshtiwan Othman
Nonlaopon, Kamsing

Journal Title

Journal ISSN

Volume Title

Publisher

Fractal and Fractional

Abstract

In this paper, we introduce the generalized left-side and right-side fractional integral operators with a certain modified ML kernel. We investigate the Chebyshev inequality via this general family of fractional integral operators. Moreover, we derive new results of this type of inequalities for finite products of functions. In addition, we establish an estimate for the Chebyshev functional by using the new fractional integral operators. From our above-mentioned results, we find similar inequalities for some specialized fractional integrals keeping some of the earlier results in view. Furthermore, two important results and some interesting consequences for convex functions in the framework of the defined class of generalized fractional integral operators are established. Finally, two basic examples demonstrated the significance of our results.

Description

Keywords

Chebyshev inequality, generalized fractional integral operators, modified ML kernel, FW function, general Wright function and its companions and extensions, synchronous functions, integral inequalities

Citation

Srivastava, H. M., Kashuri, A., Mohammed, P. O., & Nonlaopon, K. (2021). Certain inequalities pertaining to some new generalized fractional integral operators. Fractal and Fractional, 5(4), 160-181. doi.org/10.3390/fractalfract5040160.