Certain Inequalities Pertaining to Some New Generalized Fractional Integral Operators

Fractal and Fractional

Hari Mohan Srivastava¹  Pshtiwan Othman Mohammed²  Artion Kashuri³  Kamsing Nonlaopon⁴ 

[1] Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada;Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq;Department of Mathematics, Faculty of Technical Science, University “Ismail Qemali”, 9400 Vlora, Albania;Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand;

关键词: Chebyshev inequality;    generalized fractional integral operators;    modified ML kernel;    FW function;    general Wright function and its companions and extensions;    synchronous functions;   

DOI  :  10.3390/fractalfract5040160

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown