Abstract
In this present article, we establish certain new Pólya–Szegö-type tempered fractional integral inequalities by considering the generalized tempered fractional integral concerning another functionΨin the kernel. We then prove certain new Chebyshev-type tempered fractional integral inequalities for the said operator with the help of newly established Pólya–Szegö-type tempered fractional integral inequalities. Also, some new particular cases in the sense of classical tempered fractional integrals are discussed. Additionally, examples of constructing bounded functions are considered. Furthermore, one can easily form new inequalities for Katugampola fractional integrals, generalized Riemann–Liouville fractional integral concerning another functionΨin the kernel, and generalized fractional conformable integral by applying different conditions.
Highlights
PreliminariesWe consider some well-known definitions and mathematical preliminaries
In this present article, we establish certain new Polya–Szego-type tempered fractional integral inequalities by considering the generalized tempered fractional integral concerning another function Ψ in the kernel
We prove certain new Chebyshev-type tempered fractional integral inequalities for the said operator with the help of newly established Polya–Szego-type tempered fractional integral inequalities
Summary
We consider some well-known definitions and mathematical preliminaries. By setting τ 0 in (11) yields the following Riemann–Liouville fractional integral, which is defined by Definition 6 in the space (see [23]). En, the left-sided generalized tempered fractional integral of the function f1 concerning another function Ψ in the kernel is defined by. (ii) Applying Definition 6 for τ 0, it will reduce to the left-sided generalized Riemann–Liouville fractional integral operator [27]. (iii) Applying Definition 6 for Ψ(θ) ln θ, it will reduce to the following left-sided Hadamard tempered integral defined by [23]. (iv) Applying Definition 6 for Ψ(θ) θη/η, η > 0 and τ 0, it will reduce to the left-sided Katugampola [24] fractional integral. En, the one-sided generalized tempered fractional integral of the function f1 concerning another function Ψ in the kernel is defined by. If we set Ψ(X) X and τ 0, (18) will reduce to the subintegrals of Riemann–Liouville fractional integral defined by [18]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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 call
