On the weighted fractional Pólya–Szegö and Chebyshev-types integral inequalities concerning another function

Abstract

Abstract The primary objective of this present paper is to establish certain new weighted fractional Pólya–Szegö and Chebyshev type integral inequalities by employing the generalized weighted fractional integral involving another function Ψ in the kernel. The inequalities presented in this paper cover some new inequalities involving all other type weighted fractional integrals by applying certain conditions on ω ( θ ) $\omega (\theta )$ and Ψ ( θ ) $\Psi (\theta )$ . Also, the Pólya–Szegö and Chebyshev type integral inequalities for all other type fractional integrals, such as the Katugampola fractional integrals, generalized Riemann–Liouville fractional integral, conformable fractional integral, and Hadamard fractional integral, are the special cases of our main results with certain choices of ω ( θ ) $\omega (\theta )$ and Ψ ( θ ) $\Psi (\theta )$ . Additionally, examples of constructing bounded functions are also presented in the paper.

Keywords

• Fractional integrals
• Weighted fractional integrals
• Inequalities
• Chebyshev functional