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.
Highlights
IntroductionFractional calculus is the study of integrals and derivatives of arbitrary order which was a natural outgrowth of conventional definitions of calculus integral and derivative
Fractional calculus is the study of integrals and derivatives of arbitrary order which was a natural outgrowth of conventional definitions of calculus integral and derivative.There are several problems in the mathematics and its related real world applications wherein fractional derivatives occupy an important place, see [1,2,3,4,5]
We have introduced a family of generalized left-side and right-side fractional integral operators with the Wright function as the kernel
Summary
Fractional calculus is the study of integrals and derivatives of arbitrary order which was a natural outgrowth of conventional definitions of calculus integral and derivative. The Chebyshev inequality (1) is useful due to its connections with fractional calculus, and it arises naturally in the existence of solutions to various integer-order or fractional-order differential equations, including some which are useful in practical applications such as those in numerical quadrature, transform theory, statistics, and probability, see [36,37,38,39,40,41,42,43,44]. It is important to consider particular types of fractional calculus suited to the models of given real-world problems in applied mathematics. As described in many recent articles cited the fractional calculus definitions discussed in this article are useful, in modelling real-world problems
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
