Abstract
The purpose of this research paper is first to propose the generalized weighted-type fractional integrals. Then, we investigate some novel inequalities for a class of differentiable functions related to Chebyshev's functionals by utilizing the proposed modified weighted-type fractional integral incorporating another function in the kernel F(theta). For the weighted and extended Chebyshev's functionals, we also propose weighted fractional integral inequalities. With specific choices of pi(theta) and F(theta) as stated in the literature, one may easily study certain new inequalities involving all other types of weighted fractional integrals related to Chebyshev's functionals. Furthermore, the inequalities for all other type of fractional integrals associated with Chebyshev's functionals with certain choices of pi(theta) and F(theta) are covered from the obtained generalized weighted-type fractional integral inequalities.